Triangle Similarity: SSS and SAS Assignment and Quiz

Complete the statements to verify that the triangles are similar. QR/TU = __ PR/SU = __ PQ/ST = 52/13 = __ Therefore, △PQR ~ △STU by the _______ theorem.

2 2 2 SSS similarity

What value of x will make the triangles similar by the SSS similarity theorem? x =

28

What value of x will make the triangles similar by the SSS similarity theorem?

30

What value of x will make the triangles similar by the SSS similarity theorem?

77

In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8. To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that

HF is 4 units and GH is 2 units.

If △HLI ~ △JLK by the SSS similarity theorem, then HL/JL = IL/KL is also equal to which ratio?

HI/JK

Consider the two triangles. To prove that △LMN ~ △XYZ by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that

LM is 4 units and XZ is 6 units.

What additional information is needed to prove that the triangles are similar? To prove △XYZ ~ △MNO using SSS, you need to know that __________. Now that you know the length of XZ, you need to know that angle O is congruent to _________ to prove △XYZ ~ △MNO using SAS.

MN = 6 and XZ = 17.5 people angle Z

In the diagram, SQ/OM = SR/ON = 4. To prove that the triangles are similar by the SSS similarity theorem, which other sides or angles should be used?

MN and QR

Aisha is trying to determine if △LMN and △PQR are similar, congruent, or neither using the information in the diagram. Which statement is true?

NOT The triangles are similar by the SAS similarity theorem.

△RST ~ △RYX by the SSS similarity theorem. Which ratio is also equal to RT/RX and RS/RY?

ST/YX

Which statement best describes triangles UVW and XYZ?

They are similar, but not congruent.

Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ. Prove: ΔWXY ~ ΔWVZ

WX = WY; WV = WZ substitution property SAS similarity theorem

Can the triangles be proven similar using the SSS or SAS similarity theorems?

Yes, △EFG ~ △KLM by SSS or SAS.

What information is necessary to prove two triangles are similar by the SAS similarity theorem?

You need to show that two sides of one triangle are proportional to two corresponding sides of another triangle, with the included corresponding angles being congruent.

In the diagram, m∠F = 60°. To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that

angle I measures 60°

Below are statements that can be used to prove that the triangles are similar. 1. 2. ∠B and ∠Y are right angles. 3.? 4.? Which two statements are missing in steps 3 and 4?

∠B ≅ ∠Y △ABC ~ △ZYX by the SAS similarity theorem.

The ratios of corresponding sides in the two triangles are equal. What other information is needed to prove that △FGE ~ △IJH by the SAS similarity theorem?

∠I ≅ ∠F

Which pairs of triangles are similar? Check all that apply.

△DEF ~ △GHI △JKL ~ △ABC