Quadrilaterals And Proof Worksheet With Answers (Page 3 of 6) in pdf

Quadrilaterals And Proof Worksheet With Answers Page 3

To determine if the diagonals are perpendicular, use what we did to answer the first question.

Then gather more information to prove that other triangles are congruent. In particular, since

PQ ≅ RQ , QT ≅ QT , and PT ≅ RT (since the diagonal is bisected), ΔQPT ≅ ΔRQT by SSS ≅.

Because the triangles are congruent, all corresponding parts are also congruent, so

∠QTP ≅ ∠QTR. These two angles also form a straight angle. If two angles are congruent and

their measures sum to 180°, each angle measures 90°. If the angles measure 90°, the lines must

be perpendicular. Therefore, QS ⊥ PR .

Example 3

In the figure at right, if AI is the perpendicular bisector of DV , is

ΔDAV isosceles? Prove your conclusion using the two-column proof

format.

Before starting a two-column proof, it is helpful to think about what

we are trying to prove. If we want to prove that a triangle is

isosceles, then we must show that DA ≅ VA because an isosceles

triangle has two sides congruent. By showing that ΔAID ≅ ΔAIV, we

can then conclude that this pair of sides is congruent. Now that we

have a plan, we can begin the two-column proof.

Reason

Statements

(This statement is true because …)

Given

AI is the perpendicular bisector of DV

DI ≅ VI

Definition of bisector

∠DIA and ∠VIA are right angles

Definition of perpendicular

∠DIA ≅ ∠VIA

All right angles are congruent

AI ≅ AI

Reflexive Property of Equality

ΔDAI ≅ ΔVAI

SAS ≅

≅ Δs → ≅ parts

DA ≅ VA

ΔDAV is isosceles

Definition of isosceles

Parent Guide with Extra Practice

Quadrilaterals And Proof Worksheet With Answers Page 3