Final Answer:
∠1 ≅ ∠3
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Explanation:
We are given that segment RT is congruent to segment ST. That means triangle RST is an isosceles triangle, with RT and ST as the two equal sides.
In any triangle, angles opposite equal sides are also equal. So in triangle RST, side RT is opposite angle ∠3, and side ST is opposite angle ∠2. Since RT ≅ ST, then ∠2 ≅ ∠3. (That’s step 2.)
Now look at angles ∠1 and ∠2. They are vertical angles — they are formed where two lines cross (the line through R and S, and the line through T and the extension past R). Vertical angles are always congruent, so ∠1 ≅ ∠2. (That’s step 3.)
If ∠1 equals ∠2, and ∠2 equals ∠3, then by the transitive property (if A = B and B = C, then A = C), we get ∠1 ≅ ∠3. (That’s step 4.)
So the proof is complete.
Parent Tip: Review the logic above to help your child master the concept of geometry proofs worksheets two column.
