Middle School

Thank you for visiting Given ABCD is a square Prove AC perp BD We are given that ABCD is a square If we consider triangle AEB and triangle AED. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Given: \(ABCD\) is a square.

Prove: \(AC \perp BD\).

We are given that \(ABCD\) is a square. If we consider triangle \(AEB\) and triangle \(AED\), we see that side \(AB\) is congruent to side \(AD\) because sides of a square are congruent. We know that side \(AE\) is congruent to side \(AE\) by the Reflexive Property. Finally, we know that side \(BE\) is congruent to side \(DE\) because the diagonals of a square bisect each other. Therefore, triangle \(AEB\) is congruent to triangle \(AED\) by the SSS (Side-Side-Side) congruence.

We see that angle \(AED\) and angle \(AEB\) are a linear pair and congruent by CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Thus, the measure of these angles will be 90°, and diagonal \(AC\) is perpendicular to diagonal \(BD\) by definition.

Answer :

Answer:

AB

Reflexive Property

BE

SSS

Definition of perpendicular

Step-by-step explanation:

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Rewritten by : Jeany

Answer:

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.

Step-by-step explanation:

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