Geometry Final
in ABC the centroid D is on median AM. AD = x + 4 and DM = 2x - 4. Find AM
12
the sum of the interior angle measures of a polygon with s sides is 2340. find s
15
give an example of corresponding angles
angle 8 and angle 4
name the smallest angle of triangle ABC
angle B
triangle ABC has vertices A(0,10) B(4,10) and C(-2,4). find the orthocenter of triangle ABC
(-2, 12)
find the circumcenter of triangle EFG with E(4,4) F(4,2) and G(8,2)
(6, 3)
use the slope formula to determine the slope of the line containing points A(6,-7) B(9,-9)
-2/3
which three lengths could be the lengths of the sides of a triangle
10 cm 15 cm 24 cm
in quadrilateral ABCD, AE = X +6 and BE = 3x - 18. for what value of X is ABCD a rectangle
12
find the length of AB given that DB is a median of the triangle and AC = 26.
13
angle J and angle M are angles of an isosceles trapezoid JKLM. if angle J = 18X +8, and angle M = 11x + 15, find angle K
154
for the parallelogram if measurement of angle two = 4X -20 and the measurement of angle four = 3X -11 find the measurement of angle one
164
what is the measure of one interior angle in a regular 30 gon
168
DF bisects EDG. find the value of X.
19
find the measurement of angle K
The measurement of angle K = 63°
identify the transversal and classify the angle pair 11 and angle seven
The transversal line is L. the angles are corresponding angles.
find angle E and angle N, given angle F = angle P, E = (x^2)°, and N = (4x^2 - 75)°
angle E = 25° angle N = 25°
find the measurement of angle Q
angle Q = 75°
measurement of angle a equals 9X -7, measurement of angle B = 7x - 9, and measurement of angle C equals 28 - 2X. list the sides of triangle ABC in order from shortest to longest.
AB; AC; BC
DEFG is a rectangle. DF = 5X -3 and EG = X +5. find the value of X and the length of each diagonal
...
for these triangles select the triangle congruence statement and the postulate or theorem that supports it.
ABC = JKL; HL
ABC is an isosceles triangle. AB is 4X +4. BC = 8X +3 and CA = 7X +8. Find AB
AB equals 24
identify a pair of parallel segments
AB is parallel to EH
determine if the conditional statement is true. if a figure has four sides, then it is a square
false; a rectangle has four sides, and it is not a square
two sides of a triangle have lengths 6 and 17. which expression describes the length of the third side
greater than 11 and less than 23
identify the hypothesis and conclusion of the conditional statement
hypothesis: it is raining conclusion: it is cloudy
write a conditional statement from the statement a horse has four legs
if it is a horse, then it has four legs
which description does not guarantee that a quadrilateral is a square?
is a parallelogram with perpendicular diagonals
two sides of a triangle have lengths 10 and 15. what must be true about the length of the third side
less than 25
find the measure of angle ABC
measurement of angle ABC = 35°
on the measure of each numbered angle
measurement of angle one = 54°, measurement of angle 2 = 63°, measurement of angle 3 = 63°
find the measurement of angle one in the diagram
measurement of angle one equals 135°
find the measurement of angle one in the diagram
measurement of angle one equals 95°
use the slopes to determine whether the lines are parallel perpendicular or neither. AB and CD for A(3,5) , B(-2,7) , C(10,5) , and D (6,15)
neither
name the point of concurrency of the angle bisectors
not shown
classify triangle DBC by it's angle measures, given DAB = 60°, ABD = 75°, and BDC = 25°
obtuse triangle
which venn diagram is not correct
rectangles inside squares
The figure shows part of the roof structure of a house. use SAS to explain why RTS = RTU.
[1] ST = UT [2] RTS = RTU [3] RT = RT
solve the equation 4X -6 = 34
[1] addition property of equality [2] division property of equality
write a justification for each step
[1] angle addition postulate [2] division property of equality
show ABD equals CDB for A = 3
[1] A +7 [2] 4a -2 [3] 16 [4] 16 [5] SAS
The measurement of angle R = 120 and the measurement of angle S = 110. Find the measurement of angle T.
20
which three lengths cannot be the lengths of sides of a triangle?
21 m, 6m, 10 m
points B, D, and F are midpoints of the sides of ACE. EC = 30 and DF = 17. Find AC
34
LM is the midsegment of parallelogram ABCD. AB = X +8 LM = 4x + 3 DC = 243 what is the value of X
35
in a swimming pool two lanes are presented 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
Q is equidistant from the sides of TSR. find RST
42
find the length of the midsegment. the diagram is not to scale
42
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°
what is the sum of the interior angle measures of a 35 gon
5940
in the parallelogram the measurement of angle QRP = 32 and the measurement of angle PRS = 84. find PQR.
64
two sides of a triangle have lengths 5 and 12. which inequalities represent the possible lengths for the third side, x?
7 < x < 17
use the information in the diagram to determine the height of the tree
75 feet
find the value of X
8
ABF is congruent to EDG. ABF and GCS are equilateral. AG equals 21 and CG equals 1/4 AB. find the total distance from A to B to C to D to E.
98
which diagram shows a point P an equal distance from point A B and C?
A
given: ABC is congruent to MNO identify all pairs of congruent corresponding parts
A = M, B = N, C = O, AB = MN, BC = NO, AC = MO
A pilot uses triangles to find the angle of elevation A from the ground to her plane. how can she find the measurement of angle A?
ABO = CDO by SAS and angle A = angle C by CPCTC, so the measurement of angle A = 40° by substitution.
given the length Mark on the figure and AD bisects BE, use SSS to explain why ABC equals DEC.
AC = CD, AB = ED, BC = CE
given that ABC = DEC and E = 23°, find ACB
ACB = 67°
name a median for triangle ABC
BD
in ACE, G is the centroid and BE = 16. Find BG and GE.
BG = 6, GE = 12
find CA
CA = 14
for the conditional statement write the converse and a biconditional statement: a figure is a square if and only if it is a rectangle
Converse if a squared plus B squared equals C squared than the figure is a right triangle with sides A B & C biconditional: a figure is a right triangle with sides A B and C if and only if A squared plus B squared equals C squared
find DCB, given A = F, B = E and and CDE = 46°
DCB = 46°
which statement is not necessarily true? given: DE is the perpendicular bisector of JL
DK = KE
Daphne folded a triangular sheet of paper into the shape shown. find ECD, given CAB = 61°, ABC = 22° , and BCD = 42°
ECD = 41°
List the sides in order from shortest to longest
LK; LJ; JK
write a two column proof. given: T is perpendicular to L, angle one is congruent to angle 2 prove: M is parallel to L
T is perpendicular to L, angle one is congruent to angle two
determine if the biconditional is true. if false give a counterexample: a figure is square if and only if it is a rectangle
The biconditional is false. A rectangle does not necessarily have four congruent sides
to Seyfert galaxies, BW tauri and M77, represented by points A and B, are equidistant from Earth, represented by point C. What is the measurement of angle A?
The measurement of angle A = 65°
The rhombus the measurement of angle one = 140. what are the measurements of angle two and angle three?
The measurement of angle two = 140, the measurement of angle three = 20
in the rhombus the measurement of angle one = 15x, the measurement of angle two = X + Y, and the measurement of angle three equals 30Z. find the value of each variable
X = 6, Y = 84, Z = 3
find the missing values of the variables.
X = 93, Y = 74
find the value of X
X = six
write and solve inequality for X
X is greater than two
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
given RT is perpendicular to SU, SRT is congruent to URT, RS = RU, T is the midpoint of SU
[1] definition of perpendicular lines [2] third angles theorem [3] reflexive property of congruence
use the given plan to write a two column proof: given: measurement of angle one + measurement of angle two = 90°, measurement of angle 3+ measurement of angle four = 90°, measurement of angle two = measurement of angle three
[1] measurement of angle 3+ measurement of angle four = 90° [2] substitution property [3] subtraction property of equality
fill in the blanks to complete the two column proof. given: angle one and angle two are supplementary the measurement of angle 1 = 135°
[1] measurement of angle one equals 135° [2] definition of supplementary angles [3] subtraction property of equality
write a justification for each step given that EG = FH
[1] segment addition postulate [2] substitution property of equality
Given: angle 1+2 = 180° prove: L is parallel to 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
what is the name of the segment inside the large triangle
altitude
write the definition as a bike biconditional: an acute angle is an angle whose measure is less than 90°
an angle is acute if and only if it's measures less than 90°
find angle one angle three in the kite
angle one = 17 angle three = 73
find the measure of the numbered angles in the rhombus
angle one = 90, angle two = 24, angle three = 66
what type of angle pair is Angle one angle four
angle one angle four are corresponding angles
use the converse of the corresponding angles postulate and angle one is congruent to angle two to show that L is parallel to M
angle one is congruent angle two is given. from the diagram angle one and angle two are corresponding angles. so by the converse of the corresponding angles postulate L is parallel to M
use the information measurement of angle 1 is (3x + 30)° and measurement of angle 2 = (5x-10)°, and x = 20, and the theorems you have learned to show that L is parallel to M.
by substitution angle one equals 3×20+30 = 90° and angle two equals 5×20-10 = 90°. by the substitution property of equality angle one equals angle two equals 90°. by the converse of the alternate interior angles theorem, L is parallel M.
three security cameras were mounted at the corners of a triangular parking lot. camera one was 156 feet from camera two which was 101 feet from Camera three. cameras one and three were 130 feet apart. which camera had to cover the greatest angle?
camera three
write the conditional statement and converse within the biconditional: a rectangle is a square if and only if all four sides of the rectangle are equal length
conditional: if all four sides of the rectangle are equal length then it is a square Converse: if a rectangle is a square then it's four sides are equal length
write the converse, inverse, and contrapositive: if an animal is a bird, then it has two eyes
converse: if an animal has two eyes then it is a bird inverse: if an animal is not a bird then it does not have two eyes contrapositive: if an animal does not have two eyes then it is not a bird
classify triangle ABC by its side lengths
equilateral triangle
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?
seven medallions
from the ocean salmon swim perpendicularly toward the shore to lay their eggs in rivers. waves in the ocean are parallel to the shore. why must the salmon swim perpendicularly to the waves?
swimming salmon form a transversal to the shore and the waves. The shore and the waves are parallel, and the swimming salmon are perpendicular to the shore, so by the perpendicular transversal theorem, the salmon are perpendicular to the waves.
how many true conditional statements may be written using the following statements: n is a rational number. n is an integer n is a whole number
three conditional statements
identify the property that justifies the statement: AB is congruent to CD and CD is congruent to EF so AB is congruent to EF
transitive property of congruence
find the value of X
x = 45
determine if you can use HL congruence theorem to prove ACD = DBA. if not tell what else you need to know.
yes
