Home / Assignment Help / Which of following are reasons used in this proof that the equilateral triangle construction actually construct an equilateral triangle? check all that apply A) all rights angle are equal B) all of the radii of a circle are congruent C) two segments that are both congruent to a third segment must be congruent to each other D) any line segment can be extended indefinitely

Which of following are reasons used in this proof that the equilateral triangle construction actually construct an equilateral triangle? check all that apply A) all rights angle are equal B) all of the radii of a circle are congruent C) two segments that are both congruent to a third segment must be congruent to each other D) any line segment can be extended indefinitely

Answer:

SAS rule

Step-by-step explanation:

To prove: A quadrilateral ABCD is a parallelogram.

Proof: It is given that ABCD is an equilateral, thus side AB is parallel to side DC so the alternate interior angles are congruent, thus ∠ABD and ∠BDC, are congruent.

Also, From ΔADB and ΔCDB, we have

AB=DC (Given)

∠ABD =∠BDC (Alternate angles)

DB=DB (Common)

Thus, by SAS rule of congruency, ΔADB is congruent to ΔCDB that is ΔADB≅ΔCDB.

By CPCTC, ∠DBC and ∠ADB are congruent and sides AD and BC are congruent. ∠DBC and ∠ADB form a pair of alternate interior angles.

Therefore, AD is congruent and parallel to BC.

Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Hence proved.

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