Question

write a congruence statement for each figure.
19.
20.

Explanation:

Step1: Identify corresponding parts for problem 19

In figure 19, \(DG = EF\) (marked as equal), \(DE = GF\) (marked as equal), \(\angle D=\angle F = 90^{\circ}\).
By the Hypotenuse - Leg (HL) congruence criterion for right - triangles (since \(GE\) is the common hypotenuse for \(\triangle DGE\) and \(\triangle FEG\)).

Step2: Write congruence statement for problem 19

\(\triangle DGE\cong\triangle FEG\)

Step3: Identify corresponding parts for problem 20

In figure 20, \(XW = ZW\) (marked as equal), \(XY = ZY\) (marked as equal), \(\angle X=\angle Z\) (given).
By the Side - Angle - Side (SAS) congruence criterion (the included side is \(YW\) which is common to \(\triangle XYW\) and \(\triangle ZYW\)).

Step4: Write congruence statement for problem 20

\(\triangle XYW\cong\triangle ZYW\)

Answer:

1. \(\triangle DGE\cong\triangle FEG\)
2. \(\triangle XYW\cong\triangle ZYW\)