Question

Match the reasons with the statements given. Given: A = B M is midpoint of Prove: AMC BMC 1. ∠A = ∠B, M is midpoint of AB Given 2. AM = MB Sides opposite = ∠s are = 3. AC = BC SAS 4. Triangle AMC congruent to Triangle BMC Definition of midpoint

Answer 1

Proof is below.

Explanation:

Given: < A = < B , M is the midpoint of AB

Definition of midpoint: AM = MB

Sides opposite = <'s are equal: AC = BC

Triangle AMC congruent to triangle BMC: SAS

Hence, proved.

Answer 2

Answer with Step-by-step explanation:

We are given that

M is the mid point of AB

`\angle A=\angle B`

We have to match the reasons with statements given in proof.

Proof:

1.Statement:
`\angel A=\angle B`, M is the midpoint of AB

Reason: Given

2.Statement:
`AM=MB`

Reason: Definition of midpoint

3.Statement:
`AC=BC`

Reason:Opposite sides of equal angle are equal.

4.Statement:
`\triangle AMC\cong \triangle BMC`

Reason:SAS Postulate