Question

Use the diagram to complete the following tasks.

Answer 1

This exercise is about a proof in Euclidian geometry. See the explanation below.

What is Euclidian Geometry?

The study of solid and flat objects using the axioms and theorems developed by the Greek mathematician Euclid is known as Euclidean geometry (c. 300 bce).

What is the statement that completes the above proof?

Given that S is the midpoint of $\overline{QT}$:

Hence QS = TS ......................1

It is right to indicate that

PQ = TV  ........................2

And ∠RSQ is vertically opposite to ∠TSV

Hence

∠RSQ = ∠TSV.........................3

Given 1, 2, and 3,

Δ QRS ≅ ΔVTS

Therefore,

Δ QRS ≅ ΔVTS

and ∠ RSQ can be termed to be congruent to ∠TSV.

What does it mean for an angel to be congruent?

It is to be noted that the measure of an angle is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.

The angles of a regular polygon will always be congruent, regardless of its size or scale.

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