Question

Given: 4ABC, and BP is parallel to AC. Prove: m21 + m22 + m23 = 180

Answer 1

Mathematical proofs are used to prove or disprove mathematical statements.

Mathematical theorems

The theorems to use are:

• The sum of angles on a straight line is 180 degrees
• Alternate angles are congruent

The proof

From the question, we have: $\triangle ABC$

This means that, ABC is a triangle

Also, we have:

BP || AC

This means that lines BP and AC are parallel

So, the following angles are congruent by alternate angle theorem

• $\angle 5 \cong \angle 3$.
• $\angle 4 \cong \angle 2$

The angles on a straight line add up to 180 degrees.

So, we have:

$\angle 4 + \angle 1 + \angle 5 = 180$

By substitution, the above equation becomes

$\angle 2 + \angle 1 + \angle 3 = 180$

Rewrite the equation as:

$\angle 1 + \angle 2 + \angle 3 = 180$

Hence, the statement that $\angle 1 + \angle 2 + \angle 3 = 180$ has been proved

Read more about mathematical proofs at:

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