Question

Copy the proof on paper, mark the givens in the diagram, and fill in the blanks to complete the proof. Chapter Reference b If AT bisects ∠LAS, prove that ∆LAT ≅ ∆SAT. Statement Reason

LA ≅ _______

Answer 1

To prove that ΔLAT is congruent to ΔSAT given that AT bisects ∠LAS, we use Reflexive Property for congruent segments and SAS Postulate for congruence after showing the angle is bisected and sides are congruent.

Step-by-step explanation:

The question involves proving that triangles LAT and SAT are congruent if angle LAS is bisected by AT. To complete the proof provided, we first mark the given elements in a diagram, then fill in the corresponding reasons for each statement. In this scenario, the statement LA ≡ segment SA is due to the Reflexive Property, indicating that a segment is always congruent to itself.

Here's a step-by-step explanation assuming LA and SA are the congruent legs:

1. Given that AT bisects ∠LAS, we can say that ∠LAT ≡ ∠SAT by the definition of an angle bisector.
2. Because segment AT is shared between both triangles LAT and SAT, segment AT ≡ segment AT by the Reflexive Property.
3. Lastly, because we know segment LA ≡ segment SA (given), we have satisfied all three criteria for congruence by Side-Angle-Side (SAS) Postulate.
4. Therefore, ΔLAT ≡ ΔSAT by the SAS Postulate.