Geometry Final Review
Slide 77: Find the value of x. Round your answer to the nearest tenth.
x = 12.8
Slide 63: Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
x = 12; yes
A kite has angle measure of 7x degrees, 65 degrees, 85 degrees, and 105 degrees. Find the value of x. What are the measures of the angles that are congruent?
x = 15; 105 degrees
Slide 67: find the value of x. Write your answer in simplest form.
x = 16 square root 3
Slide 64: Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
x = 2 square root 30 or 11.0; no
Slide 62: Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
x = 2 square root of 34 or 11.7; no
Slide 56: Find the value of x that makes triangle ABC ~ Triangle DEF
x = 4
Slide 75: Find the value of x. Round your answer to the nearest tenth.
x = 44
Slide 29: Point D is the incenter of triangle LMN. Find the value of x.
x = 5
Slide 65: find the value of x. Write your answer in simplest form.
x = 6 square root 2
Slide 66: find the value of x. Write your answer in simplest form.
x = 7
Slide 76: Find the value of x. Round your answer to the nearest tenth.
x = 9.3
Slide 104: Find the value(s) of the variable(s)
y = 30, z = 10
Slide 58: Determine whether AB is parallel to CD
yes
Quadrilateral QXYZ is a trapezoid with one pair of congruent base angles. Is QXYZ an isosceles trapezoid? Explain your reasoning.
yes; Use the Isosceles Trapezoid Base Angles Converse
Verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse? 6,8, and 9
yes; acute
Verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse? 13, 18, and 3 square root of 55
yes; obtuse
Verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse? 10, 2square root of 2, and 6 square root of 3
yes; right
Find the coordinates of the intersection of the diagonals of QRST with vertices Q(-8,1), R(2,1), S(4,-3), T(-6,-3)
(-2,-1)
Slide 29: Find the coordinates of the circumcenter of the triangle with the given vertices: t(-6,-5), U(0,-1), V(0,-5)
(-3,-3)
Find the coordinates of the centroid of the triangle with the given vertices. A(-10,3), B(-4,5), C(-4,1)
(-6,3)
Find the coordinates of the vertices of the midsegment triangle for the triangle with the given vertices. A(-6,8), B(-6,4), C(0,4)
(-6,6), (-3,6), (-3,4)
Find the coordinates of the vertices of the midsegment triangle for the triangle with the given vertices. D(-3,1), E(3,5), F(1,-5)
(0,3), (2,0), (-1,-2)
Find the coordinates of the centroid of the triangle with the given vertices. D(2,-8), E(2,-2), F(8,-2)
(4,-4)
Slide 29: Find the coordinates of the circumcenter of the triangle with the given vertices: X(-2,1), Y(2,-3), Z(6,-3)
(4,3)
Find the lengths of the diagonals of rectangle WXYZ where WY = -2x + 34 and XZ = 3x - 26
10
Slide 113: Find the value of x
10
slide 60: find the length of AB
10.5
Slide 94: Use the diagram to find the measure of the indicated arc: KL
100 degrees
Slide 123: find the area of the kite or rhombus
105 square units
Slide 108: Find the value of x
106
Slide 59: Find the length of YB
11.2
Slide 133: Find the volume of the solid
11.34 m3
Slide 92: Point Y and Z are points of tangency. Find the value of the variable.
12
Slide 121: find the area of the kite or rhombus
130 square units
Slide 31: Find the value of x
133
Two similar triangles have a scale factor of 3:5. The altitude of the larger triangle is 24 inches. What is the altitude of the smaller triangle?
14.4 in
Find the geometric mean of the two numbers. 9 and 25
15
Slide 33: find the value of x
15
The angle between the bottom of a fence and the top of a tree is 75 degrees. the tree is 4 feet from the fence. How tall is the tree? Round your answer to the nearest foot.
15 ft
Slide 109: Find the value of x
16
Slide 94: Use the diagram to find the measure of the indicated arc: KM
160 degrees
Slide 118: Find the area of the blue-shaded region.
169.65 square in
Slide 119: Find the area of the blue-shaded region.
17.72 square in
Slide 120: Find the area of the blue-shaded region.
173.166 square ft
Slide 90: Point Y and Z are points of tangency. Find the value of the variable.
2
Slide 91: Point Y and Z are points of tangency. Find the value of the variable.
2
Slide 51: Find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality: Triangle XYZ ~ Triangle RPQ
2/5; x is congruent to r, y is congruent to p, z is congruent to q RP/XY = PQ = YZ = RQ/XZ
Find the area of ABC with the given side lengths and included angle: angle C = 79 degrees, a = 25, b = 17
208.6 square units
Slide 26: Indicated measure. Explain your reasoning: DC
20; Point B is equidistant from A and C, and BD is perpendicular to AC. So, by the Converse of the Perpendicular Bisector Theorem, DC = AD = 20
A mountain bike tire has a diameter of 26 inches. to the nearest foot, how far does the tire travel when it makes 32 revolutions?
218 ft
Slide 27: Indicated measure. Explain your reasoning: RS
23; angle PQS is congruent to angle RQS, SR is perpendicular to QR, and SP is perpendicular to QP. So, by the Angle Bisector Theorem, SR = SP. This means that 6x + 5 = 9x - 4, and the solution is x = 3. So, RS = 9(3) - 4 = 23
Find the geometric mean of the two numbers. 36 and 48
24 square root 3 or 41.6
Slide 110: Line l is tangent to the circle. Find the measure of XYZ
240 degrees
Slide 100: In the diagram QN = QP = 10, JK = 4x, and LM = 6x - 24. Find the radius of circle Q.
26
Slide 46: Find the length of the midsegment of trapezoid ABCD
26
Slide 117: Find the indicated measure: arc length of arc AB
26.09 in
Slide 106: Find the value(s) of the variable(s)
28
Slide 112: Find the value of x
3
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 6 meter, 9 meters
3 m is less than x is less than 15 m
Find the length of the midsegment of trapezoid JKLM with vertices J(6,10), K(10,6), L(8,2), and M(2,2).
3 square root of 5
Slide 50: Find the scale factor. Then list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality: ABCD ~ EFGH
3/4; A is congruent to E, b is congruent to f, c is congruent to g, d is congruent to h EF/AB = FG/BC = GH/CD = EH/AD
Slide 115: Find the indicated measure: diameter of circle P
30 ft
Two similar triangles have a pair of corresponding sides of length 12 meters and 8 meters. The larger triangle has a perimeter of 48 meters and an area of 180 square meters. Find the perimeter and area of the smaller triangle.
32 m; A = 80 m^2
A cellular telephone tower casts a shadow that is 72 feet long, while a nearby tree that is 27 feet tall casts a shadow that is 6 ft long. How long is the tower?
324 ft
Slide 41: Find the value of x that makes the quadrilateral a parallelogram.
4
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 4 inches, 8 inches
4 in. is less than x is less than 12 in
Find the area of ABC with the given side lengths and included angle: angle B = 124 degrees, a = 9, c = 11
41.0 square units
Find the area of ABC with the given side lengths and included angle: angle A = 68 degrees, b = 13, c = 7
42.2 square units
Slide 28: Indicated measure. Explain your reasoning: measure of JFH
47 degrees; Point J is equidistant from FG and FG. So by the Converse of the Angle Bisector Theorem, the measure of JFH = measure of angle JFG = 47 degrees
Slide 103: Find the value(s) of the variable(s)
5
Slide 111: Find the value of x
5
Find the sum of the measures of the interior angels of a regular 30-gon. Then find the measure of each interior angle and each exterior angle.
5040 degrees; 168 degrees; 12 degrees
Slide 116: Find the indicated measure: circumference of circle F
56.57 cm
Find the geometric mean of the two numbers. 12 and 42
6 square root 14 or 22.4
Slide 94: Use the diagram to find the measure of the indicated arc: LM
60 degrees
Slide 97: Find the measure of AB
61 degrees
Slide 98: Find the measure of AB
65 degrees
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 11 feet, 18 feet
7 ft is less than x is less 29 ft
slide 61: find the length of AB
7.2
Slide 107: Find the value of x
70
Slide 101: Find the value(s) of the variable(s)
80
Slide 94: Use the diagram to find the measure of the indicated arc: KN
80 degrees
Slide 32: find the value of x
82
Slide 99: Find the measure of AB
91 degrees
Slide 122: find the area of the kite or rhombus
96 square units
Solve ABC: angle B = 102 degrees, angle C = 43 degrees, b = 21
A = 35, a = 12.3, c = 14.6
Solve ABC: a = 10, b = 3, c = 12
A = 42.6, B = 11.7, C = 125.7
Slide 84: Solve the right triangle. round decimal answers to the nearest tenth
A = 48.2, B = 41.8, BC = 11.2
Write an indirect proof of the statement "In triangle XYZ, if XY = 4 and XZ = 8, then YZ is greater than 4"
Assume temporarily that YZ is not greater 4. Then, it follows that either YZ is greater 4 or YZ = 4. If YZ is greater 4, then XY + YZ = XZ because 4 + 4 = 8. Both conclusions contradict the Triangle Inequality Theorem, which says that XY + YZ is greater than XZ. So, the temporary assumption that YZ is not greater 4 cannot be true. This proves that in triangle XYZ, if XY = 4 and XZ = 8, then YZ is greater than 4
Solve ABC: A = 112 degrees, a = 9, b = 4
B = 24.3, C = 43.7, c = 6.7
Show that quadrilateral WXYZ with vertices W(-1,6), X(2,8), Y(1,0), and Z(-2,-2) is a parallelogram.
Because WX = YZ = the square root of 13, WX is congruent to YZ. Because the slopes of WX and YZ are both 2/3, they are parallel. WX and YZ are opposite sides that are both congruent and parallel. So, WXYZ is a parallelogram by the Opposite Sides Parallel and Congruent Theorem
Solve ABC: angle A = 28 degrees, angle B = 64 degrees, c = 55
C = 88, a = 25.8, b = 49.5
Slide 53: Show that the triangles are similar. Write a similarity statement.
C is congruent to f and b is congruent to e, so triangle ABC ~ triangle DEF
Slide 85: Solve the right triangle. round decimal answers to the nearest tenth
L = 53, ML = 4.5, NL = 7.5
Three vertices of parallelogram JKLM are J(1,4), K(5,3), and L(6,-3). Find the coordinates of vertex M.
M(2,-2)
Slide 38: State which theorem you can use to show that the quadrilateral is a parallelogram.
Parallelogram Diagonals Converse
Slide 39: State which theorem you can use to show that the quadrilateral is a parallelogram.
Parallelogram Opposite Angles Converse
Slide 37: State which theorem you can use to show that the quadrilateral is a parallelogram.
Parallelogram Opposite Sides Converse
Let Q be an acute angle. Use a calculator to approximate the measure of Q to the nearest tenth of a degree. tan Q = 0.04
Q = 2.3
Let Q be an acute angle. Use a calculator to approximate the measure of Q to the nearest tenth of a degree. sin Q = 0.91
Q = 65.5
Let Q be an acute angle. Use a calculator to approximate the measure of Q to the nearest tenth of a degree. cos Q = 0.32
Q = 71.3
Slide 52: Show that the triangles are similar. Write a similarity statement.
Q is congruent to T and RSQ is congruent to UST, so triangle RSQ ~ triangle UST
Slide 30: If RQ = RS and the measure of QRT is greater than the measure of angle SRT, then how does QT compare to ST?
QT is greater ST
Slide 55: Use the SSS Similarity Theorem or the SAS Similarity Theorem to show that the triangles are similar.
QU/QT = QR/QS = UR/TS, so triangle QUR ~ QTS
Solve ABC: angle C = 48 degrees, b = 20, c = 28
a = 99.9, b = 32.1, a = 37.1
Slide 86: Solve the right triangle. round decimal answers to the nearest tenth
X = 46.1, Z = 43.9, XY = 17.3
Slide 35: Find the value of each variable in the parallelogram
a = 28, b = 87
Slide 34: Find the value of each variable in the parallelogram
a = 79, b = 101
Slide 114: A local park has a circular ice skating rink. You are standing at point A, about 12 ft from the edge of the rink. The distance from you to a point of tangency on the rink is about 20 ft. Estimate the radius of the rink.
about 10.7 ft
Slide 134: Find the volume of the solid
about 100.53 mm3
A platter is in the shape of a regular octagon with a an apothem of 6 in. Find the area of the platter.
about 119.29 in^2
Slide 125: find the area of the kite or rhombus
about 167.11 square units
Slide 124: find the area of the kite or rhombus
about 201.20 square units
Slide 135: Find the volume of the solid
about 27.53 yd3
Slide 126: find the area of the kite or rhombus
about 37.30 square units
Solve ABC: angle B = 25 degrees, a = 8, c = 3
b = 5.4, A = 141.4, C = 13.6
Slide 36: Find the value of each variable in the parallelogram
c = 6, d = 10
Slide 54: Use the SSS Similarity Theorem or the SAS Similarity Theorem to show that the triangles are similar.
c is congruent to c and CD/CE = CB/CA, so triangle CBD ~ triangle CAE
Slide 87: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P: line segment NM
chord
Slide 96: Tell whether the red arcs are congruent. Explain why or why not.
congruent; the circles are congruent and m of arc AB = m of arc EF
write sin 72 degrees in terms of cosine
cos18
Slide 87: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P: line segment KN
diameter
Slide 89: Tell whether the common tangent is internal or external
external
Slide 40: Find the values of x and y that make the quadrilateral a parallelogram.
x = 1, y = 6
Tell whether the orthocenter of the triangle with the given vertices is inside, on, or outside the triangle. Then find the coordinates of the orthocenter. G(1,6), H(5,6), J(3,1)
inside; (3,5.2)
Slide 88: Tell whether the common tangent is internal or external
internal
Slide 105: Find the value(s) of the variable(s)
m = 44, n = 39
Slide 45: Find the measure of each angle in the isosceles trapezoid WXYZ.
measure of Z = measure of Y = 58 degrees, measure of angle W = measure of angle W = measure of angle X = 122 degrees
Slide 57: Determine whether AB is parallel to CD
no
Slide 95: Tell whether the red arcs are congruent. Explain why or why not.
not congruent; the circles are not congruent
Tell whether the orthocenter of the triangle with the given vertices is inside, on, or outside the triangle. Then find the coordinates of the orthocenter. K(-8,5), L(-6,3), M(0,5)
outside; (-6,-1)
Slide 43: Classify the special quadrilateral. Explain your reasoning.
parallelogram; there are two pairs of parallel sides
Slide 102: Find the value(s) of the variable(s)
q = 100, r = 20
Slide 82: Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
r = 4, s = 2.9
Slide 87: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P: line PK
radius
Slide 87: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P: line segment PN
radius
Slide 130: Describe the cross section formed by the intersection of the plane and solid.
rectangle
Decide whether JKLM with vertices J(5,8), K(9,6), L(7,2), and M(3,4) is a rectangle, a rhombus, or a square. Give all names that apply. Explain
rectangle, rhombus, square; the diagonals are congruent and perpendicular
Slide 49: Give the most specific name for the quadrilateral. Explain your reasoning.
rectangle; there are four right angles
Slide 42: Classify the special quadrilateral. Explain your reasoning.
rhombus; there are 4 congruent sides
Slide 48: Give the most specific name for the quadrilateral. Explain your reasoning.
rhombus; there are four congruent sides
Slide 83: Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
v = 9.4, w = 3.4
Slide 81: Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
s = 31.3, t = 13.3
Slide 87: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P: line NL
secant
Slide 78: Find sin X, sin Z, cos X, and cos Z. Write each answer as a fraction and as a decimal rounded to four decimal places.
sin X = 3/5 = 0.6, sin Z = 4/, cos X = 4/5, cos Z = 3/5
Slide 80: Find sin X, sin Z, cos X, and cos Z. Write each answer as a fraction and as a decimal rounded to four decimal places.
sin X = 55/73, sin Z = 48/73
Slide 79: Find sin X, sin Z, cos X, and cos Z. Write each answer as a fraction and as a decimal rounded to four decimal places.
sin X = 7 square root 149/149, sin Z = 10 square root 149/149 cos X = 10 square root 149/149, cos Z = 7 square root 149/149
write 29 degrees in terms of sine
sin61
Slide 131: Describe the cross section formed by the intersection of the plane and solid.
square
Slide 44: Classify the special quadrilateral. Explain your reasoning.
square; there are four congruent sides and the angles are 90 degrees
Slide 74: Find the tangents of the acute angles in the right triangle. Write each answer as a fraction and as a decimal rounded to four decimal places.
tan A = 7 square root 2/8 or 1.2374, tan B = 4 square root 2/7 or 0.8081
Slide 72: Find the tangents of the acute angles in the right triangle. Write each answer as a fraction and as a decimal rounded to four decimal places.
tan J = 11/60 or 0.1833, tan L = 60/11 or 5.4545
Slide 73: Find the tangents of the acute angles in the right triangle. Write each answer as a fraction and as a decimal rounded to four decimal places.
tan N = 12/35 or 0.3429, tan O = 35/12 or 2.9167
Slide 87: Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of circle P: ray JL
tangent
Slide 93: Tell whether line segment AB is tangent to circle C. Explain
tangent; 20^2 + 48^2 = 52^2
Slide 30: If RQ = RS and QT is greater ST, than how does angle QRT compare to angle SRT?
the measure of angle QRT is greater than the measure of angle SRT
Slide 47: Give the most specific name for the quadrilateral. Explain your reasoning.
trapezoid; there is one pair of parallel sides
Slide 132: Describe the cross section formed by the intersection of the plane and solid.
triangle
Slide 68: Identify the similar triangles. Then find the value of x.
triangle GFH ~ triangle FEH ~ triangle GEF; x = 13.5
Slide 69: Identify the similar triangles. Then find the value of x.
triangle KLM ~ triangle JKM ~ triangle JLK; x = 2 square root 6 or 4.9
Slide 70: Identify the similar triangles. Then find the value of x.
triangle QRS ~ triangle PQS ~ triangle PRQ; x = 3square root 3 or 5.2
Slide 71: Identify the similar triangles. Then find the value of x.
triangle TUV ~triangle STV ~ triangle SUT; x = 25
