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Byju's Answer

Standard VII

Mathematics

Equal Angles Subtend Equal Sides

State true or...

Question

State true or false:

In parallelogram $A B C D$ . $E$ and $F$ are mid-points of the sides $A B$ and $C D$ respectively. The line segments $A F$ and $B F$ meet the line segments $E D$ and $E C$ at points $G$ and $H$ respectively, then
triangles $H E B$ and $F H C$ are congruent.

True

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False

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Solution

The correct option is A True
Given: parallelogram $A B C D$ , E and F are mid points of $A B$ and $C D$ respectively. DE and EC meet AF and BF respectively at G and H
Now, In $△ H E B$ and $△ H F C$
$∠ E H B = ∠ F H C$ (vertically opposite angles)
$E B = F C$ (Half lengths of equal sides)
$∠ H B E = ∠ H F C$ (Alternate angles for parallel sides AB and CD)
Thus, $△ H E B ≅ △ H C F$ (AAS rule)

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State true or false:In parallelogram ABCD.E and F are mid-points of the sides AB and CD respectively. The line segments AF and BF meet the line segments ED and EC at points G and H respectively, thentriangles HEB and FHC are congruent.

State true or false:

In parallelogram $A B C D$ . $E$ and $F$ are mid-points of the sides $A B$ and $C D$ respectively. The line segments $A F$ and $B F$ meet the line segments $E D$ and $E C$ at points $G$ and $H$ respectively, then
triangles $H E B$ and $F H C$ are congruent.