Question

geometry : homework
congruence in right triangle
date 11/12/25
period
determine if the two triangles are congruent. if they are, state how you know.

1. (congruent by sss same side
2. sas
3. sss
4. sas

5)
6)

1. hl

8)

Explanation:

1. Problem Analysis:

• This problem is about triangle congruence. We need to check if the given triangles are congruent and state the congruence criterion.
• The congruence criteria for triangles are \(SSS\) (Side - Side - Side), \(SAS\) (Side - Angle - Side), \(ASA\) (Angle - Side - Angle), \(AAS\) (Angle - Angle - Side), and \(HL\) (Hypotenuse - Leg for right - triangles).

1. Solution:

• 1)
• Explanation: The two triangles have three pairs of equal sides.
• Criterion: \(SSS\) (Side - Side - Side) congruence criterion.
• 2)
• Explanation: There are two pairs of equal sides and the included angle is equal.
• Criterion: \(SAS\) (Side - Angle - Side) congruence criterion.
• 3)
• Explanation: Three pairs of equal sides (by observing the markings on the sides of the triangles formed by the diagonal of the quadrilateral).
• Criterion: \(SSS\) (Side - Side - Side) congruence criterion.
• 4)
• Explanation: Two pairs of equal sides and the included angle (the vertical angles are equal).
• Criterion: \(SAS\) (Side - Angle - Side) congruence criterion.
• 5)
• Explanation: Three pairs of equal sides (by the markings on the sides).
• Criterion: \(SSS\) (Side - Side - Side) congruence criterion.
• 6)
• Explanation: There is not enough information to prove congruence. The given side - side - angle (non - included angle) does not satisfy any of the congruence criteria (\(SSA\) is not a valid congruence criterion for non - right triangles).
• Criterion: Not congruent.
• 7)
• Explanation: These are right - triangles. The hypotenuse and one leg are equal (by the markings).
• Criterion: \(HL\) (Hypotenuse - Leg) congruence criterion.
• 8)
• Explanation: There is not enough information to prove congruence. We only know one pair of sides is equal (the vertical sides) and no information about angles or other sides to satisfy \(SSS\), \(SAS\), \(ASA\), \(AAS\), or \(HL\) (if they were right - triangles, which is not indicated).
• Criterion: Not congruent.

Answer:

1. Congruent by \(SSS\).
2. Congruent by \(SAS\).
3. Congruent by \(SSS\).
4. Congruent by \(SAS\).
5. Congruent by \(SSS\).
6. Not congruent.
7. Congruent by \(HL\).
8. Not congruent.