Question

5)
a triangle abc and a triangle xyz. can the triangles be proven congruent? yes no reason for congruence: sss sas asa aas hl aaa ass congruence statement: △abc≅△ ______
6)
a triangle abc and a triangle afc. can the triangles be proven congruent? yes no reason for congruence: sss sas asa aas hl aaa ass congruence statement: △abc≅△ ______
7)
a quadrilateral abzc with triangle abc and triangle azc. can the triangles be proven congruent? yes no reason for congruence: sss sas asa aas hl aaa ass congruence statement: △abc≅△ ______
8)
a quadrilateral abcd with triangle abc and triangle adc. can the triangles be proven congruent? yes no reason for congruence: sss sas asa aas hl aaa ass congruence statement: △abc≅△ ______
9)
a triangle abe with intersection point c. can the triangles be proven congruent? yes no reason for congruence: sss sas asa aas hl aaa ass congruence statement: △abc≅△ ______
10)
a triangle abc and a triangle fde. can the triangles be proven congruent? yes no reason for congruence: sss sas asa aas hl aaa ass congruence statement: △abc≅△ ______

Explanation:

5)

Step1: Check congruence criteria

We are given two triangles. In \(\triangle ABC\) and \(\triangle XYZ\), we have two sides and a non - included angle. The ASS (Angle - Side - Side) is not a valid congruence criterion.

6)

Step1: Check congruence criteria

In \(\triangle ABC\) and \(\triangle AFC\), we have \(AC = AC\) (common side), \(\angle BAC=\angle FAC\) (if we assume \(AC\) is the angle bisector or by construction), and \(AB = AF\) (given). But we need to check the congruence rule. However, if we consider the right - triangle case (if \(\angle ABC=\angle AFC = 90^{\circ}\)), we still don't have enough information. But if we assume it's a general triangle, we have two sides and the included angle. \(AB = AF\), \(AC=AC\) (common), \(\angle BAC=\angle FAC\) (if we assume symmetry). But actually, we have \(AB = AF\), \(BC = FC\) (by construction in the figure, assume equal marks represent equal lengths), \(AC = AC\) (common). So, by SSS (Side - Side - Side) criterion.

7)

Step1: Check congruence criteria

In \(\triangle ABC\) and \(\triangle AZC\), \(AB = AZ\) (given), \(BC = ZC\) (given), \(AC=AC\) (common). By SSS (Side - Side - Side) congruence criterion.

8)

Step1: Check congruence criteria

In \(\triangle ABC\) and \(\triangle ADC\), \(AB = AD\) (given), \(BC = DC\) (given), \(AC = AC\) (common). By SSS (Side - Side - Side) congruence criterion.

9)

Step1: Check congruence criteria

In \(\triangle ABC\) and \(\triangle DEC\), \(\angle ABC=\angle DEC\) (given), \(BC = EC\) (given if marks represent equality), \(\angle ACB=\angle DCE\) (vertically opposite angles). By AAS (Angle - Angle - Side) congruence criterion.

10)

Step1: Check congruence criteria

In \(\triangle ABC\) and \(\triangle DFE\), \(\angle ABC=\angle DFE\) (given), \(\angle BAC=\angle FDE\) (given), \(BC = FE\) (if we assume the non - marked sides are equal based on the figure's construction). But we need to check the order. By AAS (Angle - Angle - Side) congruence criterion.

Answer:

1. NO
2. YES, SSS, \(\triangle AFC\)
3. YES, SSS, \(\triangle AZC\)
4. YES, SSS, \(\triangle ADC\)
5. YES, AAS, \(\triangle DEC\)
6. YES, AAS, \(\triangle DFE\)