Question

What are the steps for Given: △ABC is a right triangle, △ADC is a right triangle, ∠ABC is a right angle, ∠ADC is a right angle and AD ≅ AB.
Prove: △ABC≅△ADC.

Answer 1

Proof (two-column):

Statements
1. ∠ABC and ∠ADC are right angles.
2. ΔABC and ΔADC are right triangles.
3. AB ≅ AD.
4. AC ≅ AC.
5. ΔABC ≅ ΔADC.

Reasons
1. Given.
2. Definition of right triangle (a triangle with a right angle).
3. Given.
4. Reflexive property of congruence (a segment is congruent to itself).
5. In right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and the corresponding leg of another right triangle, the triangles are congruent (Hypotenuse-Leg congruence theorem).

Explanation (paragraph): Since ∠ABC and ∠ADC are right, both triangles are right triangles. The hypotenuse AC is common to both triangles so AC ≅ AC, and by hypothesis AB ≅ AD. By the Hypotenuse-Leg (HL) theorem for right triangles, ΔABC ≅ ΔADC.