Question

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

Explanation:

Step1: Identify congruent triangles for problem 19

In the first figure, for triangles \( \triangle DGE\) and \( \triangle FEG\):

• \(DG = FE\) (marked with one tick)
• \(DE = FG\) (marked with two ticks)
• \( \angle D=\angle F = 90^{\circ}\)

By Hypotenuse - Leg (HL) congruence criterion (for right - angled triangles, if the hypotenuse and one leg are equal, the triangles are congruent), \( \triangle DGE\cong\triangle FEG\)

Step2: Identify congruent triangles for problem 20

In the second figure, for triangles \( \triangle XYW\) and \( \triangle ZYW\):

• \(XY = ZY\) (marked with one tick)
• \(XW = ZW\) (marked with two ticks)
• \( \angle XYW=\angle ZYW = 90^{\circ}\)

By Hypotenuse - Leg (HL) congruence criterion (for right - angled triangles, if the hypotenuse and one leg are equal, the triangles are congruent), \( \triangle XYW\cong\triangle ZYW\)

Answer:

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