Question

are the $\delta$s $\cong$? (if so, state why.
10)
11)
12)
13)
14)
15)
16)
17)
18)

Explanation:

Step1: Analyze Problem 10

The two triangles in problem 10 have all three corresponding sides marked as equal (SSS congruence criterion). So by SSS, the triangles are congruent.

Step2: Analyze Problem 11

Both triangles in problem 11 have all three corresponding sides equal (SSS), so they are congruent by SSS.

Step3: Analyze Problem 12

The figure in problem 12 shows a parallelogram divided into two triangles by a diagonal. In a parallelogram, opposite sides are equal and the diagonal is common, so by SSS (or SAS, as alternate interior angles are equal), the triangles are congruent.

Step4: Analyze Problem 13

The two triangles in problem 13 have two sides equal and the included right angle equal (SAS, since right angles are congruent), so they are congruent by SAS.

Step5: Analyze Problem 14

The triangles in problem 14 have two sides equal and the included angle equal (SAS, or also SSS as all sides seem equal), so they are congruent (e.g., SSS or SAS).

Step6: Analyze Problem 15

The triangles in problem 15 share a vertical angle, and have two sides equal (marked), so by SAS (vertical angles are congruent), they are congruent.

Step7: Analyze Problem 16

The quadrilateral is a kite - like figure, and the diagonal divides it into two triangles with two sides equal (adjacent sides of the kite) and the diagonal common, so by SSS, the triangles are congruent.

Step8: Analyze Problem 17

The two triangles in problem 17 have two angles equal (marked) and one side equal (marked), so by AAS (or ASA), they are congruent.

Step9: Analyze Problem 18

The two triangles in problem 18 have two angles equal (marked) and the included side equal (marked), so by ASA, they are congruent.

Answer:

• 10) Congruent by SSS.
• 11) Congruent by SSS.
• 12) Congruent (e.g., SSS or SAS).
• 13) Congruent by SAS.
• 14) Congruent (e.g., SSS or SAS).
• 15) Congruent by SAS.
• 16) Congruent by SSS.
• 17) Congruent by AAS (or ASA).
• 18) Congruent by ASA.