honors geometry exam semester 1

Find the measure of the supplement of <R, where m<R = (8z + 10)°

(170-8z)°

Find the coordinates of the midpoint of CM with endpoints C(1, -6) and M(7,5)

(4, -1/2)

Three vertices of a parallelogram WXYZ are X(-2, -3), Y(0,5), and Z(7,7). Find the coordinates of vertex W.

(5,-1)

M is the midpoint of AN, A has coordinates (-6,-6), and M has coordinates (1,2). Find the coordinates of N.

(8,10)

Draw and label a pair of opposite rays FG and FH

(straight line) point G then point F then point H

An animated film artist creates a simple scene by translating a kite against a still background. Write a rule for the translation of kite 1 to kite 2.

(x,y) -> (x - 6, y + 6)

Use the slope formula to find the slope of the line containing the points (-3,1) and (2,1)

0/5 = zero

Find the measure of each numbered angle

1- 54° 2- 63° 3- 63°

The map shows a linear section of Highway 35. Today, the Ybarras plan to drive the 360 miles from Springfield to Junction City. They will stop for lunch in Roseburg, which is at the midpoint of the trip. If they have already traveled 55 miles this morning, how much farther must they travel before they stop for lunch?

125 mi

Tell whether a triangle can have sides with lengths, 5, 11, and 7. Explain why

16>7 18>5 12>11 Yes, all sides work

Tell if measures 6, 14, and 13 can be side lengths of a triangle. If so, classify the triangle as acute, right, or obtuse.Explain why

20 > 13 27 > 6 205> 196 Acute, 196 isnt larger than 205 making it acute

A satellite completely orbits Earth in 216 days. Determine the angle through which the satellite travels over a period of 12 days .

20°

An angle measures 2 degrees more than 3 times its complement. Find the measure of its complement.

22°

The rectangles on a quilt are 2 in. wide and 3 in. long. The perimeter of each rectangle is made by a pattern of red thread. If there are 30 rectangles in the quilt, how much red thread will be needed?

300 in.

Vanessa wants to measure the width of a reservoir. She measures a triangle at one side of the reservoir as shown in the diagram. What is the width of the reservoir(BC across the base)?

300 m

In a swimming pool, two lanes are represented by lines l and m. If a string of flags strung across the lanes is represented by transversal t, and x = 10, show that the lanes are parallel

3x + 4 = 3(10) + 4 = 34°; 4x - 6 = 4(10) -6 = 34° The angles are alternate interior angles, and they are congruent, so the lanes are parallel by the Converse of the Alternate Interior Angles Theorem.

The diagram shows the approximate distances from Houston to Dallas and from Austin to Dallas. What is the range of distances, d, from Austin to Houston?

40 < d < 440

How many customers must both stores have before the total money they have is equal

5 customers

one of the acute angles in a right triangle has a measure of 34.6°. what is the measure of the other acute angle?

55.4°

Find the value of x. (triangle)

6

A jeweler creates triangular medallions by bending pieces of silver wire. Each medallion is an equilateral triangle. Each side of a triangle is 3 cm long. How many medallions can be made from a piece of wire that is 65 cm long?

7 medallions

Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(4,-2) to U(-2,3).

7.8 units

Tell whether a triangle can have sides with lengths 3, 4, and 8. Explain why

7> 8 12> 3 11>4 No, one side length is larger than the other two when added

Use the converse of the corresponding angles postulate and <1 ≅ <2 to show that l ∥m

<1 ≅ <2 is given. From the diagram, <1 and <2 are corresponding angles. So by the Converse of the Corresponding Angles Postulate, l ∥m

The tip of the pendulum at rest sits at point B. During an experiment, a physics student sets the pendulum in motion. The tip of the pendulum swings back and forth along the circular path from point A to point C. During each swing the tip passes through point B. Name all the angles in the diagram.

<AOB, <COB, <AOC

What additional information do you need to prove △ABC ≅ △ADC by the SAS postulate? Be specific and name the part using correct notation

<BCA ≅ <DCA

Name all pairs of vertical angles

<JLK and <MLN, <JLM and <KLN

△ABC is an isosceles triangle. AB is the longest side with length 8x+5. BC = 4x + 4 and CA = 3x + 9. Find AB

AB = 45

Determine if you can use ASA to prove △CBA ≅ △CED. Explain.

AC ≅ DC is given. <CAB ≅ <CDE because both are right angles. By the vertical angles theorem, <ACB ≅ <DCE. Therefore △CBA ≅ △CED by ASA.

Find the measures of BC and AC

BC = 6.4, AC = 4.6

Find the length of BC (number line)

BC = 7

Use the information m<1 = (3x + 30)°, m<2 = (5x-10)°, and x = 20, and the theorems you have learned to show that l ∥m.

By substitution, m<1 = 3(20) + 30 = 90° and m<2 = 5(20) - 10 = 90°. By the substitution property of equality, m<1 = m<2 = 90° By the converse of the alternate interior angles theorem, l ∥m.

Find the circumference and area of the circle. Use 3.14 for pi, and round your answer to the nearest tenth.

C = 25.1 ft; A = 50.2 ft^2

Find CA

CA = 14

Given the lengths marked on the figure and that AD bisects BE, use SSS to explain why △ABC ≅ △DEC. Be specific and name the parts using correct notation.

CD ≅ CA, AB ≅ ED, BC ≅ EC, △ABC ≅△DEC by SSS

D is between C and E. CE = 6x, CD = 4x + 8, and DE = 27. Find CE

CE = 105

K is the midpoint of JL. JK = 6x and KL = 3x + 3. Find JK, KL, and JL.

JK = 6, KL = 6, JL = 12

Write the sides △IJK in order from shortest to longest.

KJ, IK, IJ

MNOP is a parallelogram. Find MP

MP = 30

KL = MN and <KLM ≅ <MNK. Determine if the quadrilateral must be a parallelogram, Justify your answer.

No, Only one set of angles and sides are given as congruent. The conditions for a parallelogram are not met.

Name three collinear points

R, G, and N

The diagram shows the parallelogram shaped component that attaches a car's rearview mirror to the car. In parallelogram RSTU, UR = 25, RX = 16, m<STU = 42.4°. Find ST, XT, and m<RST

ST = 25, m<RST = 137.6°, XT = 16

Identify the transformation. Then use arrow notation to describe the transformation.

The transformation is a 90° rotation. ABC -> A' B' C'

The yield sign has a shape of an equilateral triangle with side lengths of 36 inches. What is the height of the sign? Will a rectangular metal sheet of 36 x 32 inches be big enough to make one sign?

The yield sign is about 31.2 inches tall. So the rectangular metal sheet will be big enough to make one sign.

The size of a tv screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27″. TV screen?

W = 21.6″ H = 16.2″

Given that YW bisects <XYZ and WZ = 4.23, find WX

WX = 4.23

Given △ABC with AB = 3, BC = 5, and CA = 6, find the length of midsegment XY.

XY = 1.5

Given: P is the midpoint of TQ and RS Prove: △TPR ≅ △QPS

[1] Definition of midpoint [2] <TPR ≅ <QPS [3] SAS

Write a two column proof given: m<1 + m<2 = 180° prove: l ∥m

[1] Vertical Angle Theorem [2] Converse of the Same side Interior Angles Theorem

Tom is wearing his favorite bowtie to the school dance. The bowtie is in the shape of two triangles. given: AB ≅ ED, BC ≅ DC, AC ≅ EC, <A ≅ <E prove: △ ABC ≅ △EDC

[1] Vertical Angles Theorem [2] Third Angles Theorem [3] △ABC ≅ △EDC

Write a two column proof. Given: t ⊥ l, <1 ≅ <2 Prove: m ∥ l

[1] t ⊥ l, <1 ≅ <2 [2] 2 intersecting lines form linear pair of ≅ <s -> lines ⊥ [3] 2 lines ⊥ to the same line -> lines ∥

a) Name a pair of corresponding angles b) Name the pairs of alternate interior angles c) Name the pairs of same side interior angles d) Name the pairs of alternate exterior angles

a) <7/<3, <8/<4, <5/<1, <6/<2 b)<1/<7, <2/<8 c) <1/<8, <2/<7 d) <3/<5, <4/<6

a) identify a pair of parallel segments b) identify a pair of skew segments c) identify a pair of perpendicular segments

a) AB ∥ DC b) DC/ EA c) GC ⊥ CD

The supplement of an angle is 26 more than five times its complement. Find the measure of the angle

angle = 74°

A right triangle is formed by the x-axis, the y-axis and the line y = -2x + 3. Find the length of the hypotenuse. Round your answer to the nearest hundreth.

d = √45/4 or 3.35

Classify △ABC by its side lengths

equilateral triangle

Determine whether the lines 12x + 3y = 3 and y = 4x + 1 are parallel, intersect, or coincide. Show your work!

intersect/ slopes are same

Tell whether the polygon is regular or irregular. tell whether it is concave or convex

irregular and concave

Graph the line y - 3 = 4(x-6)

line goes through 6,0

Find m<1 in the diagram. (Hint: Draw a line parallel to the given parallel lines.)

m<1 = 85°

A billiard ball bounces off the sides of a rectangular billiards table in such a way that <1 ≅ <3, <4 ≅ <6, and <3 and <4 are complementary. If m<1 = 26.5°, find m<3, m<4, and m<5.

m<3 = 26.5°, m<4 = 63.5°, m<5 = 53°

Two seyfert galaxies, BW Tauri and M77, represented by points A and B, are equidistant from Earth, represented by point C. what is m<A?

m<A = 65°

Find m<ABC. Name the theorem or postulate that allows you to find the measure of the angle.

m<ABC = 35 Corresponding Angles Postulate

Compare m<ABC and m<CBD.

m<ABC > m<CBD

BD bisects <ABC, m<ABD = (7x-1)°, and m<DBC = (4x+8)°. Find m<ABD.

m<ABD = 20°

GIven that △ABC ≅ △DEC and m<E = 23°, find m<ACB

m<ACB = 67°

AO and DO are the angle bisectors of <DAB and <BDA, respectively. CD ≅ BD ≅ AB, m<C = 40°. Find m<BAO.

m<BAO = 10°

Find the measure of <BOD. Then, classify the angle as acute, right, or obtuse.

m<BOD = 90°; right

Find m<DCB, given <A ≅ <F, <B ≅ <E, and m<CDE = 46°

m<DCB = 46°

Find m<E and m<N, given m<F = m<P, m<E = (x^2)°, and m<N = (4x^2 - 75)°

m<E = 25° m<N = 25°

Daphne folded a triangular sheet of paper into the shape shown. find m<ECD, given m<CAB = 61°, m<ABC = 22° , and m<BCD = 42°

m<ECD = 41°

Find m<K

m<K = 63°

m<IJK = 57° and m<IJL = 20°. Find m<LJK

m<LJK = 37°

Find m<Q

m<Q = 75°

Find m<RST. Name the theorem or postulate that allows you to find the angle.

m<RST = 72 theorem = Alternate Exterior Angles Theorem

Find the value of n in the triangle

n = 11

Use the slopes to determine whether the lines are parallel, perpendicular, or neither. Show your work! AB and CD for A(3,5), B(-2,7), C(10,5) and D(6,15)

neither

Classify △DBC by its angle measures, given m<DAB = 60°, m<ABD = 75°, and m<BDC = 25°

obtuse triangle

Tell whether <1 and <2 are only adjacent, adjacent and form a linear pair, or not adjacent.

only adjacent

Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.

polygon, decagon

Find the missing side length. Tell if the side length form a Pythagorean triple. Explain why

side length - 15 Yes, can be Pythagorean triple all sides came out as a whole number

Given: △ABC ≅ △MNO Identify all pairs of congruent corresponding parts.

sides: AB ≅ MN, BC ≅ NO, AC ≅ MO angles: <A ≅ <M, <B ≅ <N, <C ≅ <O

Use the slope formula to determine the slope of the line.

slope = -2/3

In △ABC, show that midsegment KL is parallel to AB and that KL = 1/2 AB.

slopes: (parallel) KL = 1/4 and AB = 1/4 AB = 8.2 KL = 4.1 so KL = 1/2 AB

Milan starts at the bottom of a 1000 foot hill at 10:00 am and bikes to the top by 3:00 pm. graph the line that represents Milans distance up the hill at a given time. Find and interpret the slope of the line.

the slope is 200, so Milan traveled 200 feet per hour

Identify the transversal and classify the angle pair <11 and <7

transversal: L corresponding angles

name two lines in the figure

wc and cr

Find the values of x and y. Express your answers in simplest radical form.

x = 12 y = 12√3

Find the value of x so that m // n. Name the theorem or postulate that allows you to find x.

x = 17 Converse of Same Side Interior Angles Theorem

Find the value of x (2.5x + 6)

x = 21.6

Each triangle is a 45° - 45° - 90° triangle. find the value of x.

x = 3√2/2

Find the value of x. Express your answer in simplest radical form.

x = 3√5

An isosceles triangle has a perimeter of 50 cm. The congruent sides measure (2x + 3) cm. The length of the third side is 4x cm. What is the value of x?

x = 5.5

Find the value of x. Express your answer in simplest radical form. (all fractions)

x = 5√2/2

Write and solve an equality for x.

x>2

Write an equation of a line with slope 2 and passing through the point (4,7) in point-slope form.

y - 7 = 2(x-4)

Write an equation of the line through (-3,-4) with slope 2/3 in slope-intercept form.

y = 2/3x - 2

two sides of an equilateral triangle measure (2y + 3) units and (y^2 - 5) units. if the perimeter of the triangle is 33 units what is the value of Y?

y = 4

Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A(-2,2) and B(5,4)

y-3 = -7/2(x-1.5)

for these triangles select the triangle congruence statement and the postulate or theorem that supports it.

△ABC ≅ △JKL, HL