Question

geometry
assignment
date: 2/11/24
period 2
determine if the two triangles are congruent. if they are, state how you know.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)

Explanation:

Step1: Analyze triangle pair 1

Triangles share hypotenuse, have 1 pair of equal legs, right angles.
Right triangles: HL (Hypotenuse-Leg) congruence.

Step2: Analyze triangle pair 2

Triangles share a side, have 2 pairs of equal sides.
SSS (Side-Side-Side) congruence.

Step3: Analyze triangle pair 3

Triangles have 1 pair of equal sides, 1 pair of equal angles, but sides are not corresponding.
No congruence (insufficient matching parts).

Step4: Analyze triangle pair 4

Triangles share hypotenuse, have 1 pair of equal legs, right angles.
Right triangles: HL (Hypotenuse-Leg) congruence.

Step5: Analyze triangle pair 5

Triangles have vertical equal angles, 2 pairs of equal sides (SAS).
SAS (Side-Angle-Side) congruence.

Step6: Analyze triangle pair 6

Triangles share a side, have 1 pair of equal sides, 1 pair of equal angles (SAS).
SAS (Side-Angle-Side) congruence.

Step7: Analyze triangle pair 7

Triangles share a side, have 1 pair of equal sides, 1 pair of equal angles (SAS).
SAS (Side-Angle-Side) congruence.

Step8: Analyze triangle pair 8

Triangles share hypotenuse, have 1 pair of equal legs, right angles.
Right triangles: HL (Hypotenuse-Leg) congruence.

Step9: Analyze triangle pair 9

Triangles share a side, have 2 pairs of equal sides.
SSS (Side-Side-Side) congruence.

Step10: Analyze triangle pair 10

Triangles have 1 pair of equal sides, no matching angles/corresponding sides.
No congruence (insufficient matching parts).

Step11: Analyze triangle pair 11

Triangles have vertical equal angles, 2 pairs of equal angles (AA, but no matching sides).
No congruence (insufficient matching sides).

Step12: Analyze triangle pair 12

Triangles have 1 pair of equal sides, 1 pair of equal angles, but sides are not corresponding.
No congruence (insufficient matching parts).

Answer:

1. Congruent, HL
2. Congruent, SSS
3. Not congruent
4. Congruent, HL
5. Congruent, SAS
6. Congruent, SAS
7. Congruent, SAS
8. Congruent, HL
9. Congruent, SSS
10. Not congruent
11. Not congruent
12. Not congruent