Question

17)
can the triangles be proven congruent?
yes no
reason for congruence:
sss sas asa aas hl aaa ass
congruence statement: △abc≅△ ______
18)
can the triangles be proven congruent?
yes no
reason for congruence:
sss sas asa aas hl aaa ass
congruence statement: △abc≅△ ______
19)
can the triangles be proven congruent?
yes no
reason for congruence:
sss sas asa aas hl aaa ass
congruence statement: △abc≅△ ______
20)
can the triangles be proven congruent?
yes no
reason for congruence:
sss sas asa aas hl aaa ass
congruence statement: △abc≅△ ______

Explanation:

17)

Step1: Analyze the given information

We have two right - angled triangles \( \triangle ABC\) and \( \triangle DBE\). \(AB = DB\) (given as equal segments), \(AC=DE\) (given as equal segments), and \( \angle ABC=\angle DBE = 90^{\circ}\).

Step2: Apply the congruence criterion

By the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles (where the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle).

Step1: Analyze the angles and sides

We know that \(AB\) is a common side. Let's assume \( \angle ABC\) and \( \angle ABD\) are related. But we have two angles and a non - included side. However, \( \angle CAB=\angle DAB\) (common angle), \(AB = AB\) (common side), and we cannot be sure about the other sides and angles in a way that satisfies a valid congruence criterion. AAA (angle - angle - angle) is not a valid congruence criterion (it only shows similarity) and ASS (angle - side - side) is not a valid congruence criterion for non - right - angled triangles.

Step1: Analyze the given information

We have \( \angle BAC=\angle DCA\) (given as equal angles), \(AC = AC\) (common side), and \( \angle BCA=\angle DAC\) (given as equal angles).

Step2: Apply the congruence criterion

By the Angle - Side - Angle (ASA) congruence criterion (where two angles and the included side of one triangle are equal to two angles and the included side of another triangle)

Answer:

YES, HL, \( \triangle DBE\)

18)