Question

complete the triangle congruence statement in order to prove the given statement. what postulate or theorem would you use (sss, sas, hl, aas or asa)? given (overline{bc}congoverline{ad}) diagram congruence statement (\triangle abccong\triangle) method

Explanation:

Step1: Identify the right - angled triangles

We have two right - angled triangles \(\triangle ABC\) and \(\triangle DCA\). In \(\triangle ABC\) and \(\triangle DCA\), \(\overline{BC}\cong\overline{AD}\) (given), \(\overline{AC}\cong\overline{AC}\) (common side).

Step2: Apply the Hypotenuse - Leg (HL) theorem

For right - angled triangles (the right angles are \(\angle BAC\) and \(\angle DCA\)), if the hypotenuse and one leg of a right - angled triangle are congruent to the hypotenuse and one leg of another right - angled triangle, then the two right - angled triangles are congruent. Here, in right - angled triangles \(\triangle ABC\) and \(\triangle DCA\), the hypotenuse \(BC = AD\) and the common leg \(AC\) is shared.

Answer:

Congruence Statement: \(\triangle ABC\cong\triangle DCA\)
Method: \(HL\) (Hypotenuse - Leg)