Question

5.1 - 5.4 worksheet
name:
state the method of congruence. (sss, sas, hl, asa, aas)
1.
2.
3.
4.
5.
6.
7.
8.
state the method of congruence, and then finish the statement: ( \triangle abccong\triangle )____.

Explanation:

Step1: Recall Congruence Criteria

• SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.
• HL (Hypotenuse - Leg): For right - angled triangles, if the hypotenuse and a leg of one right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle, the triangles are congruent.

Step2: Analyze Each Pair

1. Problem 1:

• There are three pairs of equal sides. So, the congruence method is \(SSS\).

1. Problem 2:

• There is a right - angle (implied by the right - angled look), one pair of equal sides and one pair of equal angles (the non - right angles). But if we consider the two sides and the included angle (the non - right angle), it is \(SAS\).

1. Problem 3:

• Two angles and the included side are equal. So, the congruence method is \(ASA\).

1. Problem 4:

• Two angles and a non - included side are equal. So, the congruence method is \(AAS\).

1. Problem 5:

• There is a right - angle (the perpendicular), one pair of equal sides (the common side) and the hypotenuse (the sides of the big triangle). So, it is \(HL\).

1. Problem 6:

• Three pairs of equal sides. So, the congruence method is \(SSS\).

1. Problem 7:

• Three pairs of equal sides (as marked). So, the congruence method is \(SSS\).

1. Problem 8:

• Two angles and the included side are equal. So, the congruence method is \(ASA\).

Answer:

1. \(SSS\)
2. \(SAS\)
3. \(ASA\)
4. \(AAS\)
5. \(HL\)
6. \(SSS\)
7. \(SSS\)
8. \(ASA\)