Question 1
Question 2
Given the diagram above, is the following statement true or false?
There is not enough information to prove the triangles are congruent.
Question 3
Fill In The Blanks. (Use A Symbol In Your Answers.) 11. Which Triangles Are Similar According To The AA Similarity Theorem?
Answer to question 1
A, C, and D are true
Answer to question 2
Given the digram, you are required to check if the following statement is true or false. There is not enough information to prove the triangles are congruent.
First, we must perform an analysis of the given figure.
- Segment OTOT and segment AZAZ are congruent.
- Angle OO is congruent to angle AA.
- TPTP and ZPZP are congruent because they are bisected by segment OAOA. Therefore, the point PP is the midpoint of segment TZTZ.
- Since the segments OTOT and AZAZ are congruent, and the segments TPTP and ZPZP are also congruent. We can say that the angles TT and ZZ are congruent.
- Angles OO and TT are connected by segment OTOT.
- Angles AA and ZZ are connected by segment AZAZ.
- We prove that the triangles OTPOTP and AZPAZP are congruent, using the angle, side, angle (ASA) postulate.
According to the analysis of the figure, we can determine that there is information to prove that the triangles are congruent. Therefore, statement “There is not enough information to prove the triangles are congruent” is FALSE.
Answer to question 3
