Right Triangle congruence Worksheet for 9th - 10th Grade | Lesson ... - Free Printable

You're right to point out that I can't see the image you uploaded. Since I don’t have access to visual content, I can’t analyze the specific triangles shown in your worksheet.

However, I can help you solve any “Right Triangle Congruence” problem by explaining the rules and giving you a step-by-step method to check for congruence yourself.

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## 🔍 How to Determine if Two Right Triangles Are Congruent

There are 5 main congruence postulates/theorems for triangles — but for right triangles, we have 2 special ones plus the general ones:

✔ Special Right Triangle Congruence Theorems:

1. HL (Hypotenuse-Leg)
→ If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
*Only works for right triangles.*

2. HA (Hypotenuse-Angle)
→ If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another, the triangles are congruent.
*(This is really AAS applied to right triangles.)*

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✔ General Triangle Congruence Theorems (also work for right triangles):

3. SAS (Side-Angle-Side)
→ Two sides and the included angle are congruent.

4. ASA (Angle-Side-Angle)
→ Two angles and the included side are congruent.

5. AAS (Angle-Angle-Side)
→ Two angles and a non-included side are congruent.

> ⚠️ SSA does NOT guarantee congruence — unless it’s HL (which is a special case of SSA for right triangles).

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## 📐 Step-by-Step Guide to Solve Your Worksheet

Since I can’t see your image, here’s how YOU can solve each pair:

For Each Pair of Triangles (labeled 1–10):

1. Check if both are right triangles.
→ Look for the right-angle symbol (□) or assume it’s given since the worksheet says “Right Triangle Congruence.”

2. Compare corresponding parts:
- Are the hypotenuses equal? (longest side opposite the right angle)
- Are any legs equal? (sides forming the right angle)
- Are any angles equal? (especially acute angles)

3. Match to a congruence theorem:
- If you see hypotenuse + leg → use HL
- If you see hypotenuse + acute angle → use HA (or AAS)
- If you see two legs → use SAS (since the right angle is between them)
- If you see leg + adjacent acute angle → use ASA or AAS

4. Write your answer:
- “Congruent by HL”
- “Congruent by SAS”
- “Not congruent” — if no matching theorem applies

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## 💡 Example (Made Up — You Apply This to Your Image)

Suppose you have two right triangles:

- Triangle A: legs = 3 and 4, hypotenuse = 5
- Triangle B: legs = 3 and 4, hypotenuse = 5

→ They are congruent by SAS (the right angle is between the two legs), or even SSS, or HL.

Another example:

- Triangle C: hypotenuse = 10, leg = 6
- Triangle D: hypotenuse = 10, leg = 6

→ Congruent by HL

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## 🧩 What to Do Now

Since I can’t see your image, please describe one pair at a time like this:

> “Pair #1: Both are right triangles. One has legs 5 and 12, the other has hypotenuse 13 and leg 5.”

Then I’ll tell you if they’re congruent and why.

Or, if you can describe what each pair looks like (e.g., “both have right angles, one leg marked equal, hypotenuse marked equal”), I can guide you through all 10!

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✔ Bottom Line: Use HL, SAS, ASA, AAS — avoid SSA unless it’s HL. Look for matching sides/angles and apply the correct theorem.

Let me know how you’d like to proceed — describe the triangles, or ask about a specific pair!