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

Sagot :

MrRoyal

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: [tex]\triangle ABC[/tex]

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

  • [tex]\angle 5 \cong \angle 3[/tex].
  • [tex]\angle 4 \cong \angle 2[/tex]

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

So, we have:

[tex]\angle 4 + \angle 1 + \angle 5 = 180[/tex]

By substitution, the above equation becomes

[tex]\angle 2 + \angle 1 + \angle 3 = 180[/tex]

Rewrite the equation as:

[tex]\angle 1 + \angle 2 + \angle 3 = 180[/tex]

Hence, the statement that [tex]\angle 1 + \angle 2 + \angle 3 = 180[/tex] has been proved

Read more about mathematical proofs at:

https://brainly.com/question/25296908

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