234k views
4 votes
Solve the following problem:

Given: △SAL, SA = LA

AT − ∠bisector

Prove: m∠L = m∠S

Solve the following problem: Given: △SAL, SA = LA AT − ∠bisector Prove: m∠L = m∠S-example-1
User Chouser
by
7.7k points

2 Answers

4 votes

Explanation:

First, we know that △ALT ≅ △AST, because of Side Angle Side Theorem. Next, we know that AL ≅ AS, because it's given.

Since A = A, we can remove A and it gives us m∠L = m∠S.

If you need to show work in math terms, your answer should look something like this:

1. △ ALT ≅ △AST - SAS

2. AL ≅ AS - Given

3. m∠ L ≅ m∠S

Hope this helped!

User Jianweichuah
by
7.6k points
5 votes

Answer:


\angle L=\angle S using congruence rule

Explanation:

Given: ΔSAL, SA = LA and AT is the bisector of
\angle A

To prove:
\angle L=\angle S

Proof:

Two triangles are congruent if they have same shape and same size.

Consider triangles ALT and AST

AL = AS

As AT bisects
\angle A,
\angle LAT=\angle SAT\\

AT = AT (common side)

So,
\Delta ALT\cong \Delta AST ( by SAS congruence rule )

Here, SAS denotes side-angle-side


\angle L=\angle S (using corresponding parts of congruent triangles)

Hence proved

User AYESIGYE DERRICK
by
7.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories