In the figure, A B C D is a parallelogram. C E bisects ∠ C and A F bisects ∠ A . Is ∠ A = ∠ C ? If the statement is true, give its reason.

The given figure is Here it is given that A B C D is a parallelogram. We know that, Opposite angles of a parallelogram are equal. Here, ∠ A is the opposite angle of ∠ C . ⇒ ∠ A = ∠ C . Hence, the statement is true.

In the figure, A B C D is a parallelogram. C E bisects ∠ C and A F bisects ∠ A . Is ∠ C E B = ∠ F A B ? If the statement is true, give its reason.

The given figure is ∠ A = ∠ C (opposite angles of a parallelogram are equal) ⇒ 1 2 ∠ A = 1 2 ∠ C So, we can write ∠ F A B = ∠ D C E . . . . . . . . . i Now A B is parallel to D C (opposite sides are parallel) ∠ C E B = ∠ D C E . . . ( i i ) (Alternate interior angles) From equation i and i i , ∠ F A B = ∠ C E B Hence, the statement is true.

E M B I B E

Number Magic a textbook of Mathematics 8>Chapter 5 - Special Types of Quadrilaterals>EXERCISE>Q 13

MEDIUM

8th CBSE

IMPORTANT

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If the sum of two opposite angles of a parallelogram is $110 °$ , find the measure of its angles.

Important Questions on Special Types of Quadrilaterals

EASY

8th CBSE

IMPORTANT

Number Magic a textbook of Mathematics 8>Chapter 5 - Special Types of Quadrilaterals>EXERCISE>Q 14

In the figure, $A B C D$ is a parallelogram. $C E$ bisects $∠ C$ and $A F$ bisects $∠ A$ .

Question Image

Is $∠ A = ∠ C ?$ If the statement is true, give its reason.

EASY

8th CBSE

IMPORTANT

Number Magic a textbook of Mathematics 8>Chapter 5 - Special Types of Quadrilaterals>EXERCISE>Q 14

In the figure, $A B C D$ is a parallelogram. $C E$ bisects $∠ C$ and $A F$ bisects $∠ A$ .

Question Image

Is $∠ C E B = ∠ F A B ?$ If the statement is true, give its reason.

MEDIUM

8th CBSE

IMPORTANT

Number Magic a textbook of Mathematics 8>Chapter 5 - Special Types of Quadrilaterals>EXERCISE>Q 14

In the figure, $A B C D$ is a parallelogram. $C E$ bisects $∠ C$ and $A F$ bisects $∠ A$ . In each of the following, if the statement is true, give reason.