Question

Match the following items.

Given:
ABC
AC = BC
Prove:
3 = 1


1. AC = BC
Base ∠'s of isosceles triangle =
2. ∠1 = ∠2
1
Given
3. ∠2 = ∠3
Vertical angles =
4. ∠1 = ∠3
Substitution

Answer 1

1.
`AC=BC` ------- (Given)

2.
`\angle 1=\angle 2` --------- Base ∠'s of isosceles triangle =

3.
`\angle 2=\angle 3` ---------- Vertical angles

4.
`\angle 1=\angle 3` ---------- Substitution

Explanation:

We have been given an image of triangle ABC. We are asked to prove that measure of angle 1 is equal to measure of angle 3.

Step 1:

`AC=BC` ------- (Given)

Step 2:

`\angle 1=\angle 2` --------- Base ∠'s of isosceles triangle =

Since AC is equal to BC, this means triangle ABC is an isosceles triangle, so its base angles or angles corresponding to these side will be equal, therefore, measure of angle 1 is equal to angle to by base angles of an isosceles triangle.

Step 3:

We can see from our given diagram that angle 2 and angle 3 are vertical angles, therefore
`\angle 2=\angle 3` ---------- Vertical angles.

Step 4:

Using substitution property of equality we will get,
`\angle 1=\angle 3`.