Geometry Questions

For the right triangles below find the values of the side lengths a and c Round your answers to the nearest tenth 45 a a 0 C 45 7 X 60 5 30 8

AB BG AC GC LABC LGBC G B T 1 What rigid transformation will take triangle GBC onto triangle ABC 2 Explain why G will coincide with A 3 Is triangle GBC congruent to triangle ABC Explain your reasoning

A translation is applied to triangle PQR to create triangle P Q R 10 8 6 L a Select O 20 10 8 a 2 L 8 10 Q D 2 4 6 Let the statement x y a b describe the translation Create equations for a in terms of x and for b in terms of y that could be used to describe the translation 8 10

2 AB and AD are tangent to circle Q Find the value of B X 8 5x 4 Q D

Find the following in circle P K 84 P 73 N L M 3 arc MN x 3 4 4 are LM 5 ZJPN

15 Find the volume of the pyramid 20 m 30 m 24 m

0 0 AA O yes ASA O not congruent O yes SAS 00 00 00 05

Find the exact circumferenc 5 area 196 mi

Find the length of the hypotenuse Round your answer to the nearest hundredth 7 Show Your Work 4 O 9 95 8 06 3 32 O 11 00

Use these two triangles to answer questions 7 and 8 Given ZA 50 ZB 100 AABC APRO B A 14 What is mzQ OA 20 OB B 30 OC 50 O D D 100 22 4 C P 20 R 32

Required GivenDE BC Which proportion is justified by the image A 18 18 24 28 34 24 32 8 O 18 24 O 18 24 24 8 8 O 18 2 4 24 D 6 C E 8 B

Part of an ancient coin was discovered It was measured and only an 80 section of it was left If the coin had a radius of 0 9 inch what is the area of this sector of the coin in square inches 0 81 T O 0 64 T 0 36 T 0 18 T

Required Given AKLM ARST Which congruent statments would be true K M Show Your Work R OKMRT and LK ST OKMRT and LM LS OLKLR and KM RT OZKLR and ZM ZS

Find the volume of the composite figure 5 in The volume of the composite figure is 2 in 8 in cubic inches 2 in 5 in

quired What is the volume of a cylinder with base radius 2 in and a height of 5in 2 5

A x 70 76 A x 70 76 41 Show Your Work 41 B O 187 O 63 7 7

If the m FMN x 20 m FML x and m LMN 150 Find the m FMN N F M L

Based on the diagram which congruence statement is true B AC DE ZACB LEDC ZC ZD

What is csc ZA Reduce fractional answers to lowest terms A 12 5 13 B

AQRS has a perimeter of 55 If RT bisects LR What is the length of segment QT R Q 10 12 18 T 12 S

The two polygons below are similar W U 10 Complete the similarity statement D A TUVW What is the similarity ratio of the first polygon to the second polygon o cimilarity ratio and write it as a proper fraction improper fraction or wh

Required Which statement is true Ay M 8 6 4 2 8 a 2 2 4 6 8 Triangle LMN is an equilateral triangle Triangle LMN is a right scalene triangle Triangle LMN is a right isosceles triangle Triangle LMN is an acute isosceles triangle

15 Which of the following graph is Hamiltonian H A G1 B G1 G2 C G3 G4 D G4 G P m G4 4 1

Relative to angle G which side is the adjacent side E M Choose 1 answer A GE G

If the ratio for the sin Z 7071 what is the m Z Hint Use the trig table to determine this measure m Z

Which of the following has a ratio that is equal to b c a Select all that apply a b d 70 e f sin 20 cos 20 tan 20 sin 70 cos 70 tan 70 C b 20

What is cot ZB Reduce fractional answers to lowest terms 10 21 26 C

Triangle PQR is shown where ST is parallel to RQ 1 ST I RQ 2 ZPST ZR and ZPTS ZQ 3 APQR APTS 4 5 PR PS SR PQ PT TQ 6 PS SR PS B Statements 7 PS ST 8 SB TO TQ PS PT TQ PT B PT Reason 3 Select R Statement 4 Select Reason 4 Select 1 Given 2 If two parallel lines are cut by a transversal then corresponding angles are congruent 3 SR Maria wants to prove that PS Select a statement or reason in each blank to complete Maria s proof 4 5 Segment addition postulate 6 Substitution Reasons 7 Commutative property of addition 8 Subtraction property of equality TQ PT

For a given arithmetic sequence the first term a is equal to 18 and the 40th term 940 is equal to 17 Find the value of the 10th term a10 a C

Given the following unit circle rotate green dot to the appropriate angle and then find the exact value of the function sin 45 y

Identify the ratio for the cos Q Write your fraction in simpliest form P 14 R 50 Q

Parallelogram ABCD is shown Point E is the midpoint of segment AB Point F midpoint of segment CD 8 4 y 8 4 0 4 8 E 4 F 8 Which transformations carries the parallelogram onto itself a rotation of 180 degrees clockwise about the center of the parallelogram a reflection across line segment EF O a rotation of 180 degrees clockwise about the origin

A teacher draws circle O ZRPQ and ZPOQ as shown The teacher asks students to select the correct claim about the relationship betweer m RPQ and m ROQ Claim 1 The measure of ZRPQ is equal to the measure of ZROQ Claim 2 The measure of ZROQ is twice the measure of ZRPQ

Find the volume of the rectangular prism 6cm 3 c 9 cm

Find the height of the pyramid 10 1 mi 9 mi 9 mi

Solve for x 8 x Simplify your answer Type an integer or a simplified fraction

Find the surface area of the rectangular prism 6 cm 3 cm 9 cm

Question 11 Square ABCD is transformed to create image A B C D as shown 4 D C 2 4 2 y 0 A P 2 B B A 2 C D 4 X Select all of the transformations that could have been performed O a rotation of 180 degrees clockwise about the origin a reflection across the line y x O a reflection across the line y 2x O a rotation of 270 degrees counterclockwise about the origin and then reflection acros x axis

Find the area and perimeter of the following 3x Area 10 15x Perimeter 3x 5 Area 100 Perimeter 22 2x 5 Area 10x 10 Perimeter 6x 2 15x Area 6x 15 Perimeter 10x 2 10x

Circle is shown with points A B C and D on Circle O A D 20 0 C mZAOB B If z 50 what is the value of y and the angle measurement of ZAOB Drag a tile into each box degrees 4

Quadrilateral BCDE is shown on the coordinate grid Keisha reflects the figure across the line y x to create B C D E What are the coordinates of E 10 10 8 6 4 2 Y 8 6 4 2 01 2 41 6 8 10 2 B 4 6 10 8 10

Question 8 The proof shows that opposite angles of a parallelogram are congruent Statements ABCD is a parallelogram with diagonal AC ABCD and AD BC 22 23 21 24 m 2 m3 and mz1 m 4 m 1 m 2 m 4 m 2 mel m 2 m 4 m 3 m l m 2 m BAD m23 mz4 m DCB m BAD m2DCB BAD DCB What is the missing part of the proof O Angle Addition Postulate O Substitution O Alternate Interior Angles are congruent Reasons Given Definition of parallelogram Altemate interior angles are congruent Measures of congruent angles are equal Addition property of equality Angle addition postulate Substitution Angles are congruent when their measures are equal

Triangle ABC is shown Statements 1 Triangle ABC is isosceles D is the midpoint of AC 2 2 AD DC 3 3 BABC 4 4 BD exists A 5 5 BD BD 6 6 AABD ACBD 7 7 2BAC ZBCA 1 Given Reasons 2 Definition of midpoint 3 Definition of isosceles triangle 4 A single line segment can be drawn between any two points 5 6 7

Find the volume of the rectangular prism 3 m 11 m 3 m

Find the EXACT circumference of the following circle Use T you can copy and paste the symbol or write it as pi 20 cm

Which diagram shows only the first step of constructing the line perpendicular to through point P B A A P X B B D A B t t P B

below Complete both transformations Then enter the final coordinates of the figure A 2 4 C 3 1 1 3 2 2 Dilate K 4 B A 5 2 B C

6 Prove if QR a tangent of the circle S Use the Pythagorean theorem a b c R O 14 S 19 25

4 Find the value of x 9x 1 C E 41 5x D F

Find the area of the following 14 m 27 m 23 m