Geometry Name: Proof Worksheet (3) Date: 1. Given: ∠3 ≅ ∠4 ... - Free Printable

Final Answer:
∠1 ≅ ∠2

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Explanation:
Let’s look at problem #1.

We are told that ∠3 ≅ ∠4. That means angle 3 and angle 4 are equal in size.

Now, look at the picture. Points A and B are on a straight line. That means angles next to each other on that line add up to 180° — they’re called “linear pairs.”

So:
- ∠1 and ∠3 are next to each other on the straight line → they add up to 180°.
- ∠2 and ∠4 are also next to each other on the same straight line → they also add up to 180°.

That means:
∠1 + ∠3 = 180°
∠2 + ∠4 = 180°

But we know ∠3 = ∠4 (given).

So if you subtract the same amount (∠3 or ∠4) from 180°, you get the same leftover.

That means ∠1 must equal ∠2.

So, ∠1 ≅ ∠2.

It’s like saying:
If 10 - 3 = 7 and 10 - 3 = 7, then both answers are the same.
Here, 180° - ∠3 = ∠1 and 180° - ∠4 = ∠2, and since ∠3 = ∠4, then ∠1 = ∠2.

Done!