Question

sss and sas congruence
state if the two triangles are congruent. if they are, state how you know.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)

Explanation:

1)

• Step1: Analyze the triangles

The two right - angled triangles have the hypotenuse (common side) and one leg (marked with equal signs) equal.

• Step2: Apply congruence criterion

By Hypotenuse - Leg (HL) congruence (a special case for right - angled triangles, which is similar to SSS in the sense that two sides and the right - angle (which is a fixed angle of \(90^{\circ}\)) are considered). The triangles are congruent.

2)

• Step1: Identify sides and angle

Two sides (marked with equal signs) and the included angle (common angle) are equal.

• Step2: Apply congruence criterion

By Side - Angle - Side (SAS) congruence, the triangles are congruent.

3)

• Step1: Check for congruence

There is no information about the included angle or another side. Just two sides (marked) are not sufficient.

• Step2: Conclusion

The triangles are not congruent.

4)

• Step1: Check side - angle - side

The sides and the included angle do not match. One triangle has two sides and a non - included angle (if we consider the given markings), and the other has a different side - angle - side combination.

• Step2: Conclusion

The triangles are not congruent.

5)

• Step1: Analyze side lengths

The three sides (marked with equal signs) of the two triangles are equal.

• Step2: Apply congruence criterion

By Side - Side - Side (SSS) congruence, the triangles are congruent.

6)

• Step1: Check side - side - side

The three sides (marked with equal signs) of the two triangles (formed by the common line and the marked sides) are equal.

• Step2: Apply congruence criterion

By SSS congruence, the triangles are congruent.

7)

• Step1: Check side - side - side

The side lengths (marked) do not match. For example, one triangle has sides with one double - mark, one single - mark and one triple - mark (in a certain order), and the other has a different combination of side - mark lengths.

• Step2: Conclusion

The triangles are not congruent.

8)

• Step1: Identify sides and angle

Two sides (marked with equal signs) and the included angle (vertical angles are equal) are equal.

• Step2: Apply congruence criterion

By SAS congruence, the triangles are congruent.

9)

• Step1: Check right - angled triangles

One is a right - angled triangle (with a right - angle mark) and the other is not (no right - angle mark).

• Step2: Conclusion

The triangles are not congruent.

10)

• Step1: Analyze right - angled triangles

The two right - angled triangles have the hypotenuse (marked with two equal signs) and one leg (marked with one equal sign) equal.

• Step2: Apply congruence criterion

By HL congruence (a special case for right - angled triangles), the triangles are congruent.

Answer:

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