Geometry Notes - Section 4.6 Triangle Congruence CPCTC

Multiple Choice

A landscape architect sets up the triangle shown in the figure to find the distance of JK across a pond. What is JK?

• 30 ft

• 41 ft

• 19 ft

• 60 ft

Multiple Choice

An archaeologist wants to find the height AB of a rock formation. She places a marker at C and steps off the distance from C to B. Then she walks the same distance from C and places a marker at D. If DE = 6.3 m, what is AB?

• 2.1 m

• 3.8 m

• 7.2 m

• 6.3 m

Multiple Select

Which postulate can you use to prove the triangles in the image are congruent?

• HL

• SAS

• ASA

• SSS

Multiple Select

Which of the following are statements and reasons you can use to prove PQ is congruent to PS? Hint, multiple answers may be correct

• PR is congruent to PR by the reflexive proerty

• Angle QPS is congruent to SPR by angle bisector theorem

• Triangle QPR is Congruent to SPR by ASA

• PQ is congruent to PS by CPCTC

Multiple Select

Given:

1. X is the midpoint of ST

2. RX is perpendicular to ST

Prove: RS is congruent to RT by CPCTC

Hint, multiple answers may be correct

• angle RXS is 90° by the definition of perpendicular segments

• SX is congruent to RX by the definition of midpoint

• RX is congruent to RX by the reflexive property

• Triangle RXS is congruent to triangle RXT by HL postulate

Multiple Select

Prove KL is parallel to MN. Hint, multiple answers can be correct

• KJ is congruent to JM by the definition of midpoint

• LJ is congruent to JN by the definition of midpoint

• Angle KJN is congruent to LJM by the definition of vertical angles

• Triangle KJN is congruent to LJM by CPCTC

Multiple Choice

Prove that RT = JL using the distance formula

• RT = JL = $$\sqrt[]{5}$$

• RT = JL = 5

• RT = JL = $$2\ \ \sqrt[]{5}$$

• RT = JL = 2

Multiple Choice

Prove that RS = JK using the distance formula

• RS = JK = 10

• RS = JK = $$\sqrt[]{10}$$

• RS = JK = 2

• RS = JK = $$\sqrt[]{5}$$

Multiple Choice

Prove that ST = KL using the distance formula

• ST = KL = 3.8259

• ST = KL = 17

• ST = KL = $$\sqrt[]{17}$$

• ST = KL = 6.284

Multiple Choice

How is triangle JKL congruent to RST (hint, you need to know the last three question answers to know the answer)

• JKL congruent to RST by SSS

• JKL congruent to RST by SAS

• JKL congruent to RST by AAS

• JKL congruent to RST by HL

Multiple Choice

Angle JKL is congruent to angle RST by

• HL

• CPCTC

• ASA

• AAS