Fill in the blanks in the list. Main Idea: You do not need to know the measures of all pairs of congruent parts to know that two triangles are congruent. You can use the congruence. instead!

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Certainly! Based on your main idea, here's a completed list outlining the key **Triangle Congruence Criteria** that you can use to determine if two triangles are congruent without needing to measure all pairs of congruent parts:

### **Main Idea:**
You do not need to know the measures of all pairs of congruent parts to know that two triangles are congruent. You can use the **congruence criteria** instead!

### **Triangle Congruence Criteria:**

1. **Side-Side-Side (SSS):**
   - **Definition:** If all three pairs of corresponding sides of two triangles are congruent, then the triangles are congruent.
   - **Example:** If triangle ABC has sides AB ≅ DE, BC ≅ EF, and CA ≅ FD, then triangle ABC ≅ triangle DEF by SSS.

2. **Side-Angle-Side (SAS):**
   - **Definition:** If two pairs of corresponding sides and the included angles are congruent, then the triangles are congruent.
   - **Example:** If AB ≅ DE, angle B ≅ angle E, and BC ≅ EF, then triangle ABC ≅ triangle DEF by SAS.

3. **Angle-Side-Angle (ASA):**
   - **Definition:** If two pairs of corresponding angles and the included side are congruent, then the triangles are congruent.
   - **Example:** If angle A ≅ angle D, side AB ≅ DE, and angle B ≅ angle E, then triangle ABC ≅ triangle DEF by ASA.

4. **Angle-Angle-Side (AAS):**
   - **Definition:** If two pairs of corresponding angles and a non-included side are congruent, then the triangles are congruent.
   - **Example:** If angle A ≅ angle D, angle B ≅ angle E, and side BC ≅ side EF, then triangle ABC ≅ triangle DEF by AAS.

5. **Hypotenuse-Leg (HL) – *For Right Triangles*:**
   - **Definition:** 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.
   - **Example:** If in right triangles ABC and DEF, hypotenuse AB ≅ hypotenuse DE and leg BC ≅ leg EF, then triangle ABC ≅ triangle DEF by HL.

### **Summary:**
By applying these **congruence criteria**, you can efficiently determine the congruence of two triangles without needing to measure every corresponding side and angle. This approach simplifies proofs and problem-solving in geometry.
**Triangle Congruence Criteria:** 1. **SSS (Side-Side-Side):** All three sides of one triangle are congruent to all three sides of another triangle. 2. **SAS (Side-Angle-Side):** Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. 3. **ASA (Angle-Side-Angle):** Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. 4. **AAS (Angle-Angle-Side):** Two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle. 5. **HL (Hypotenuse-Leg) – for Right Triangles:** The hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle. **Summary:** Use these criteria to determine if two triangles are congruent without measuring all corresponding parts.

Fill in the blanks in the list. Main Idea: You do not need to know the measures of all pairs of congruent parts to know that two triangles are congruent. You can use the congruence. instead!

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