Three statements are given below: 1. In a Rectangle ABCD, the diagonals AC bisects as well as . 2. In a Square ABCD, the diagonals AC bisects as well as . 3. In rhombus ABCD, the diagonals AC bisects as well as . Which is True?

Three statements are given below: 1. In a Rectangle ABCD, the dia…

MCQ

Three statements are given below:

In a Rectangle ABCD, the diagonals AC bisects $\angle\text{A}$ as well as $\angle\text{C}.$
In a Square ABCD, the diagonals AC bisects $\angle\text{A}$ as well as $\angle\text{C}.$
In rhombus ABCD, the diagonals AC bisects $\angle\text{A}$ as well as $\angle\text{C}.$

Which is True?

✓

II and III
Solution:
In square and rhombus, all sides are equal. By joining the points A and C diagonal AC formed. we get two triangles ABC and ADC which are congruent (SAS congruence). Also, opposite sides are parallel. So, by using alternate angle property we can prove that angle $\text{BAC}= \angle\text{DCA}$ and angle $\text{DAC}= \angle\text{ACB}.$ But by CPCT $\angle\text{DAC}= \angle\text{BAC}.$
So, all four angles made by diagonal AC with end points A and C are equal which proves that diagonal AC bisects $\angle\text{A}$ and $\angle\text{C}$ both.

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