Question

6 using the diagram shown, choose the correct conclusion. a all of the above b the triangles are congruent by ha. c the triangles are congruent by la. d the triangles are congruent by hl.

Explanation:

Step1: Analyze the given information

We have two right - angled triangles \( \triangle RAC\) and \( \triangle YTC\). \(AC = TC\) (given as equal segments), \(RC=YC\) (given as equal segments). Also, \(\angle A=\angle T = 90^{\circ}\)

Step2: Recall congruence criteria for right - angled triangles

• HL (Hypotenuse - Leg): In a right - angled triangle, if the hypotenuse and one leg are equal to the hypotenuse and one leg of another right - angled triangle, then the two triangles are congruent. Here, \(RC\) and \(YC\) are hypotenuses (\(RC = YC\)), and \(AC\) and \(TC\) are legs (\(AC=TC\))
• HA (Hypotenuse - Angle): If the hypotenuse and an acute angle of one right - angled triangle are equal to the hypotenuse and an acute angle of another right - angled triangle, the triangles are congruent. Since \(RC = YC\) (hypotenuse) and \(\angle RCA=\angle YCT\) (vertically opposite angles, so equal), we can use HA
• LA (Leg - Angle): If a leg and an acute angle of one right - angled triangle are equal to a leg and an acute angle of another right - angled triangle, the triangles are congruent. Since \(AC = TC\) (leg) and \(\angle RCA=\angle YCT\) (vertically opposite angles, so equal), we can use LA

Answer:

A. All of the above