Question

fill in the blank 1 point
are the triangles congruent? choose your answer...
what postulate can prove these triangles are congruent? choose your answer...

Explanation:

Step1: Analyze the figure

The figure shows a rectangle divided into two triangles by a diagonal. In a rectangle, opposite sides are equal. So, we have two right - angled triangles.

Step2: Apply the congruence postulate

For right - angled triangles, the Hypotenuse - Leg (HL) postulate states that if the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent. Here, the diagonal is the hypotenuse (common to both triangles) and the sides of the rectangle (which are equal) are the legs.

Answer:

Yes, the triangles are congruent by the Hypotenuse - Leg (HL) postulate.