Question

9.
aa~ sss~ sas~ not ~
△____~△____
11.
aa~ sss~ sas~ not ~
△____~△____

Explanation:

Step1: Analyze problem 9

• We know that vertical angles are equal. So, \(\angle TUS=\angle VUW\) (vertical angles).
• We are given \(\angle T = \angle V=72^{\circ}\).
• By the AA (Angle - Angle) similarity criterion (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar).
• So, \(\triangle TSU\sim\triangle VWU\)

Step2: Analyze problem 11

• Check the ratios of the sides. \(\frac{KJ}{GJ}=\frac{87}{68}\approx1.28\) and \(\frac{LJ}{HJ}=\frac{95}{72}\approx1.32\)
• The ratios of the corresponding sides are not equal.
• There is no information about the angles (except vertical angles \(\angle KJL=\angle GJH\)), but we cannot apply AA (since we don't have a second pair of equal angles), SSS (sides ratios not equal) or SAS (sides ratios not equal) similarity.

Answer:

• For problem 9: \(AA\sim,\triangle TSU\sim\triangle VWU\)
• For problem 11: \(Not\sim\)