Question

Write a two-column proof. given: bca acd b and d are rt. prove: ∆abc ∆adc

Answer 1

See explanation

Explanation:

Consider triangles ABC and ACD. These triangles are right triangles because

`\angle B\cong \angle D=90^(\circ)\ \text{right angles}`

In these triangles:

1. 
   `\angle BCA\cong \angle ACD` - given
2. 
   `BC\cong BC` by reflexive property of equality

So,

`\triangle ABC\cong \triangle ADC` - by HA theorem.

The hypotenuse angle theorem, also known as the HA theorem, states that 'if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.'