The document Hots Questions- Areas of Parallelograms and Triangles Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by VP Classes.

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**Question 1. If two sides of one triangle are equal to the two sides of another triangle and the contained angles are supplementary; show that the two triangles are equal in area.**

Let âˆ†ABC and âˆ†DEF are such that AC = DE; CB = EF and âˆ ABC + âˆ DEF = 180Â°.

Now, allow âˆ†DEF fall along âˆ†ABC such that DE falls on AC and B and F are on opposite directions.

âˆµâˆ ACB + âˆ†DEF = 180Â°

â‡’ BCF is a straight line

âˆ´ We get a âˆ†AFB, in which C is mid point of FB.

âˆ´ AC is median of âˆ†AFB, Median divides the âˆ† into two triangles equal in area.

â‡’ ar (âˆ†AFC) = ar (âˆ†ABC)

â‡’ ar (âˆ†DEF) = ar (âˆ†ABC).

**Question 2. In a trapezium ABCD, where AB || DC, E is the mid point of BC. Prove that âˆ†AED = Â½ trap. ABCD.**

**Hint:** Through E, draw FEG || AD meeting AB and CD in F and G respectively.

âˆ´âˆ† BEF â‰… âˆ† CEG

â‡’ ar trap. ABCD = ar (||^{gm} ADGF)

â‡’ âˆ† AED = Â½ ||^{gm} ADGF

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