MATH SOLVE

9 months ago

Q:
# Given:AC = BC∠3 = ∠4Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove that triangle ACM is congruent to triangle BCM. If it is not possible to prove the triangles are congruent, choose "not possible".SSSSASASAnot possible

Accepted Solution

A:

AC = BC gives you one pair of congruent sides.

<3 = <4 gives you a pair of congruent angles.

You already have SA.

Maybe you can add another pair of congruent angles to use ASA,

or maybe you can add another pair of congruent sides to use SAS.

Now we look at the drawing and see what we can add to what we have.

We don't know anything about angles A and B to use ASA.

We see side CM which is a side of both triangles.

A segment is congruent to itself. Since side CM is a side of both triangles, that is the other pair of congruent sides.

We can use SAS.

Answer: SAS

<3 = <4 gives you a pair of congruent angles.

You already have SA.

Maybe you can add another pair of congruent angles to use ASA,

or maybe you can add another pair of congruent sides to use SAS.

Now we look at the drawing and see what we can add to what we have.

We don't know anything about angles A and B to use ASA.

We see side CM which is a side of both triangles.

A segment is congruent to itself. Since side CM is a side of both triangles, that is the other pair of congruent sides.

We can use SAS.

Answer: SAS