Question

Given: ABCD is a square.

Prove: AC ⊥ BD.



We are given that ABCD is a square. If we consider triangle AEB and triangle AED, we see that side is congruent to side AD because sides of a square are congruent. We know that side AE is congruent to side AE by using the . Finally, we know that side DE is congruent to side because the diagonals of a square bisect each other. Therefore, triangle AEB is congruent to triangle AED by congruency. We see that angle AED and angle AEB are a linear pair, and congruent by CPCTC. Thus, the measure of these angles will be 90°, and diagonal AC is perpendicular to diagonal BD by the .

Answer 1

This question is based on concept of geometry. Therefore, the answers are as follows:

1) AB 2) Reflexive property 3) BE 4) SSS

5) definition of perpendicularity.

Given that:

ABCD is a square.

In this question, we have to fill the blanks and complete the sentence where it is looking like incomplete.

According to question,

Therefore, at first It is given that, if we consider triangle AEB and Triangle AED, we observe that side AB side is congruent to side AD.

(2) We know that, side AE is congruent to side AE by using the Reflexive property because sides of a square are congruent.

(3) Finally, we know that side DE is congruent to side BE because the diagonals of a square bisect each other.

(4)Therefor triangle AEB is congruent to triangle AED by SSS congruency.

(5) We see that angle AED and angle AEB are a linear pair, and congruent by CPCT , the angle AED and AEB are a linear pair and the measure of these angle will be 90 because ABCD is a square and thus diagonal AC is perpendicular to diagonal BD by the definition of perpendicularity.

Therefore, the answers are as follows:

1)AB

2)Reflexive property

3)BE

4)SSS

5) definition of perpendicularity.

Explanation:

Answer 2

AB

Reflexive Property

BE

SSS

Definition of perpendicular

Explanation: