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djverab [1.8K]
2 years ago
12

title=" \underline{ \underline{ \text{question}}} : " alt=" \underline{ \underline{ \text{question}}} : " align="absmiddle" class="latex-formula">
In the given figure , AP = BP = PC. Prove that \angleABC = 1 rt.angle.

~Thanks in advance ! ♡

Mathematics
2 answers:
steposvetlana [31]2 years ago
8 0

Answer:

See Below.

Step-by-step explanation:

In the given figure, AP = BP = PC.

And we want to prove that ∠ABC is a right angle.

Since AP = BP and BP = PC, we can create two isosceles triangles: ΔAPB and ΔCPB.

By the definition of isosceles triangles, in ΔAPB, ∠PAB and ∠PBA are equivalent. Let the measure of each of them be <em>x°</em>.

Likewise, in ΔCPB, ∠PCB and ∠PBC are equivalent.

And since AP = BP = PC, each of the angles∠PCB and ∠PBC will also be equivalent to <em>x°.</em>

<em />

And since the sum of the interior angles of a triangle total 180°, we acquire:

\angle PAB+\angle PBA+\angle PCB+\angle PBC=180

Since they are all equivalent:

4x=180

Hence:

x=45^\circ

∠ABC is the sum of ∠PBA and ∠PBC, each of which measures 45°. Hence:

\angle ABC=\angle PBA+\angle PBC=45+45=90^\circ

Deffense [45]2 years ago
4 0

Answer:

this is your answer look it once.

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