Question

Line EIF is a line of symmetry for figure

ABECDF. Clare says that ABEF is congruent to CDFE because sides AB and CD are corresponding.
E
1. Why is Clare's congruence statement incorrect?
2. Write a correct congruence statement for the quadrilaterals.

Answer 1

Clare's congruence statement is incorrect because the sides AB and CD being corresponding is not sufficient to establish congruence between the quadrilaterals.

Corresponding sides alone do not guarantee congruence; the corresponding angles also need to be equal.

1. Why Clare's congruence statement is incorrect:

Corresponding sides alone do not guarantee congruence.

Congruence requires both corresponding sides and corresponding angles to be equal.

2. Correct Congruence Statement:

To establish congruence between quadrilaterals, both corresponding sides and corresponding angles must be equal.

If the angles and sides of ABEF and CDFE are equal, you can state: "Quadrilaterals ABEF and CDFE are congruent by SAS (Side-Angle-Side) congruence."