Similar Triangle Postulates and Theorems

Open Ended

Why do you think understanding polygons and their properties is important in mathematics?

Multiple Select

Which of the following statements are true about postulates and theorems?

• A postulate must be proven using logic.

• A theorem is accepted without proof.

• A postulate is accepted as true without proof.

• A theorem must be proven using math rules.

Multiple Choice

What is the difference between a postulate and a theorem in mathematics?

• A postulate is proven, a theorem is accepted without proof.

• A postulate is accepted without proof, a theorem is proven.

• Both are accepted without proof.

• Both are proven using logic.

Open Ended

Explain why knowing two angles of a triangle guarantees that the third angle is also determined.

Multiple Choice

Which triangle similarity criterion requires two angles in one triangle to match two angles in another triangle?

• Side-Side-Side (SSS)

• Side-Angle-Side (SAS)

• Angle-Angle (AA)

• Angle-Side-Angle (ASA)

Open Ended

Given two triangles with angles 26°, 90° and 64°, 90°, are the triangles similar? If so, state the similarity criterion used and explain your reasoning.

Multiple Choice

Which of the following statements best explains why triangles CDE and KGH are similar?

• All corresponding angles are equal, so the triangles are similar by the AA Similarity Postulate.

• All corresponding sides are equal, so the triangles are congruent.

• The triangles have the same area.

• The triangles have the same perimeter.

Multiple Choice

Which of the following is the correct matching of vertices for comparing triangles ABC, DEF, and GHJ?

• A ↔ D ↔ G, B ↔ E ↔ H, C ↔ F ↔ J

• A ↔ E ↔ H, B ↔ D ↔ G, C ↔ F ↔ J

• A ↔ F ↔ J, B ↔ D ↔ G, C ↔ E ↔ H

• A ↔ D ↔ J, B ↔ E ↔ G, C ↔ F ↔ H

Multiple Select

Select all correct side length pairs that should be compared to determine similarity between triangles ABC and DEF.

• AB and DE

• BC and EF

• AC and DF

• BC and DF

Multiple Choice

Which of the following ratios is NOT equal to 4/3 when comparing Triangle ABC and Triangle DEF?

• AB/DE

• BC/EF

• AC/DF

• AB/EF

Multiple Choice

What is the significance of having all three pairs of corresponding sides in two triangles with the same ratio?

• The triangles are congruent

• The triangles are similar by the SSS Similarity Theorem

• The triangles are right triangles

• The triangles have equal areas

Open Ended

Is either Triangle DEF or Triangle GHJ similar to Triangle ABC? Justify your answer using the SSS Theorem.

Multiple Choice

If the ratios of corresponding sides between two triangles are 1, 6/5, and 1, what can you conclude about the triangles?

• They are similar by SSS

• They are congruent

• They are not similar

• They are right triangles

Open Ended

Explain the process of determining whether two triangles are similar using the SSS (Side-Side-Side) Similarity Theorem.

Multiple Choice

Is either Triangle DEF or Triangle GHJ similar to Triangle ABC?

• Triangle DEF is similar to Triangle ABC

• Triangle GHJ is similar to Triangle ABC

• Both triangles are similar to Triangle ABC

• Neither triangle is similar to Triangle ABC

Multiple Choice

Which theorem states that if all three sides of one triangle are in the same ratio as the three sides of another triangle, then the triangles are similar?

• Side-Angle-Side Theorem

• Angle-Angle Theorem

• Side-Side-Side Theorem

• Angle-Side-Angle Theorem

Multiple Choice

Which of the following are required for two triangles to be similar by the Side-Angle-Side (SAS) Theorem?

• Two angles and one side are equal

• All three sides are in the same ratio

• One angle and the two sides that touch that angle are in the same ratio

• All angles are equal

Open Ended

Explain the difference between the Side-Side-Side (SSS) and Side-Angle-Side (SAS) similarity theorems for triangles.

Multiple Choice

Which pairs of sides are compared to check for SAS similarity in triangles EDF and YWX?

• ED and YW, DF and WX

• ED and WX, DF and YW

• EF and YX, DF and WX

• EF and YW, DE and WX

Open Ended

Determine whether △EDF and △YWX are similar by SAS. If they are similar, write a similarity statement and find the scale factor.

Multiple Choice

Which of the following is a postulate or theorem used to prove triangle similarity?

• Pythagorean Theorem

• Side-Side-Side Theorem

• Quadrilateral Postulate

• Circle Theorem