Question

Given: 1 = 2, 3 = 4, TS = TR. Name the postulate or theorem you can use to prove TKS = TLR.

A. Angle Bisector Theorem
B. Corresponding Angles Postulate
C. Side-Side-Side (SSS) Postulate
D. Alternate Interior Angles Theorem

Answer 1

Without the specific diagram (Figure 4.17 or 4.18), it is not possible to confidently select a postulate or theorem to prove triangles TKS and TLR are congruent. However, based on the given information, the Side-Angle-Side (SAS) Postulate would be considered if included among the choices. Trigonometry or Pythagorean Theorem might not be relevant here.

Step-by-step explanation:

To prove that triangles TKS and TLR are congruent, we must evaluate the information given and choose the appropriate postulate or theorem. Given that angle 1 is congruent to angle 2, and angle 3 is congruent to angle 4, we also know that side TS is equal to side TR. With two pairs of congruent angles and a pair of congruent sides not between them, we can apply the Side-Angle-Side (SAS) Postulate.

However, this option is not given in the choices. The correct answer from the provided options would depend on the specific diagram and instructions related to figure 4.17 or 4.18, which are not provided. Without the proper context or a visual representation, we cannot confidently select from options A, B, C, or D. Additionally, since the statement "TS = TR" pertains to sides and not necessarily to angles, and without additional information, trigonometry or Pythagorean Theorem may not be applicable here.