Geometry Review: Packet #3

If AC = BC in triangle ABC with m∠A = (8x − 40)° and m∠B = (5x − 1)°, find m∠C.

• 13°

• 52°

• 56°

• 64°

Which side lengths could form a triangle? Select all that apply.

• 8, 8, 17

• 2, 11, 12

• 20, 6, 15

• 19, 34, 15

Two sides of a triangle measure 24 inches and 29 inches. Which of the following could represent the third side? Select all that apply.

• 7 inches

• 31 inches

• 58 inches

• 60 inches

Two sides of a triangle measure 3 meters and 8 meters. Which inequality gives the possible values for the perimeter P of the triangle?

(a)   <x​ < (b)  

• 16
• 22
• 5
• 11
• 0
• 15

Order the sides of the triangle from least to greatest given angle measures at the vertices are m∠R = 61°, m∠S = 56°, and m∠T = 63°.

• RT

• RS

• ST

If ΔJKL ≅ ΔMNP where m∠K = (9x − 24)°, m∠L = 63°, and m∠N = (5x + 4)°, find m∠M.

• 63°

• 72°

• 78°

• 7°

Which of the following are valid methods to prove two triangles are congruent? Select all that apply.

• SSS

• SAS

• ASA

• AAS

• HL

In the diagram, KN ≅ MN and point L lies on segment KM with KL ⟂ LM, forming right triangles ΔKLN and ΔMLN with hypotenuses KN and MN and sharing leg LN. Which triangle congruence criterion proves ΔKLN ≅ ΔMLN?

• HL (Hypotenuse–Leg)

• SAS

• ASA

• AAS

Which congruence theorem is used in Step 4 to prove the triangles are congruent?

• SSS

• SAS

• ASA

• AAS

Given: KL ≅ MN and KM ≅ NL, with LM as a shared side. Prove: ΔKLM ≅ ΔNML. Which congruence theorem justifies this result?

• SSS

• SAS

• ASA

• AAS