Question

in 17 - 20, name the postulate that allows you to conclude that the triangles are congruent. (g6b)

1. △abc ≅ △dcb

17.____
18.____
18.
19.____
20.____
19.
20.

Explanation:

17.

Step1: Analyze the triangles

We have right - angled triangles \(ABC\) and \(DCB\). The hypotenuse \(AC = DB\) (marked as equal) and the leg \(BC=CB\) (common side).

Step2: Apply the congruence postulate

For right - angled triangles, if the hypotenuse and a leg are equal, we use the \(HL\) (Hypotenuse - Leg) postulate.

18.

Step1: Analyze the triangles

We have right - angled triangles. The hypotenuse and one leg of each triangle are equal (marked as equal).

Step2: Apply the congruence postulate

Since we have right - angled triangles with equal hypotenuse and leg, we use the \(HL\) postulate.

19.

Step1: Analyze the triangles

We have two triangles. The vertical angles are equal. Two pairs of sides are equal (marked as equal).

Step2: Apply the congruence postulate

Since two sides and the included angle (vertical angles are equal) are equal, we use the \(SAS\) (Side - Angle - Side) postulate.

20.

Step1: Analyze the triangles

We have three pairs of sides equal (marked as equal).

Step2: Apply the congruence postulate

If three sides of one triangle are equal to three sides of another triangle, we use the \(SSS\) (Side - Side - Side) postulate.

Answer:

1. A. \(HL\)
2. C. \(HL\)
3. B. \(SAS\)
4. A. \(SSS\)