Question

1. mark any congruent parts you can prove on the triangles. the triangles are congruent by:

a) sss ≅
b) sas ≅
c) asa ≅
d) aas ≅
e) δs are not ≅

1. mark any congruent parts you can prove on the triangles. the triangles are congruent by:

a) hl ≅
b) sas ≅
c) asa ≅
d) aas ≅
e) δs are not ≅

1. mark any congruent parts you can prove on the triangles. the triangles are congruent by:

a) hl ≅
b) sas ≅
c) asa ≅
d) aas ≅
e) δs are not ≅

Explanation:

4)

Step1: Identify congruent sides

From the figure, we can see that \(WX = WY\), \(WZ=WZ\) (common side), and \(XZ = YZ\).

Step2: Apply congruence criterion

Since all three pairs of corresponding sides are equal, we use the SSS (Side - Side - Side) congruence criterion.

Step1: Identify right angles and other parts

We have \(\angle XYW=\angle ZYW = 90^{\circ}\), \(\angle X=\angle Z\) (given), and \(YW = YW\) (common side).

Step2: Apply congruence criterion

We have two angles and a non - included side. The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, the triangles are congruent.

Step1: Identify right triangles

We have two right triangles \(\triangle MNQ\) and \(\triangle PNQ\). \(MN = PN\) (given), \(NQ=NQ\) (common side).

Step2: Apply congruence criterion

For right triangles, if the hypotenuse (\(MN = PN\)) and one leg (\(NQ\)) are equal, we use the HL (Hypotenuse - Leg) congruence criterion.

Answer:

A. \(SSS\cong\)

5)