Question

Given: AABC is a right triangle and ZDAB is a right angle.

Prove: LACB LDAC.
Note: quadrilateral properties are not permitted in this proof.
Step
1
Statement
AABC is a right triangle
LDAB is a right angle
Type of Statement
Reason
Given
A
B

Answer 1

Since
`\angle` CAB is a right angle and its complement is
`\angle` DAC,
`\angle` ACB and
`\angle` DAC are corresponding angles in similar positions to a right angle.

How to prove the angles

In a right-angled triangle, where
`\angle` DAB is a right angle, we're aiming to prove that
`\angle` ACB is equal to
`\angle` DAC.

Let's use some basic geometry principles to establish this:

Given:

Triangle ABC is a right triangle with right angle DAB.

Proof:

In a right triangle, the sum of all angles equals
`180^o`.

We know that angle DAB is a right angle (
`90^o`).

Therefore, the sum of angles DAC and CAB equals
`90^o` (since
`90^o` + x =
`180^o` , where x represents the sum of angles DAC and CAB).

Since
`\angle` CAB is a right angle and its complement is
`\angle` DAC,
`\angle` ACB and
`\angle` DAC are corresponding angles in similar positions to a right angle.

As corresponding angles are equal,
`\angle` ACB is equal to
`\angle` DAC.

This proof relies on the properties of right-angled triangles and the relationships between angles in a triangle.