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!

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.