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Chapter 5: Q2 (page 192)

For the following figure, X, Y, Z are the midpoints of the sides of isosceles ΔABC. Name two trapezoids other than XZBA.

Short Answer

Expert verified

The two trapezoids are ACZY,BCXY.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

A trapezoid is a type of quadrilateral with one pair of parallel sides.

Consider the triangle ΔABC.

Here the points Y and Z are the mid points ofAB¯ and BC¯.

03

Step 3. Step description.

Now, the side YZ¯is parallel to the third side AC¯such that YZ¯∥AC¯.

So ACZYis a quadrilateral with exactly one pair of sidesYZ¯ and AC¯parallel.

Therefore, ACZYis a trapezoid.

Here the points X and Y are the mid points ofAC¯ and AB¯.

Now, the side XY¯is parallel to the third side BC¯such that XY¯∥BC¯.

So BCXYis a quadrilateral with exactly one pair of sides XY¯and BC¯parallel.

Therefore, BCXYis a trapezoid.

Thus, the two trapezoids are ACZYand BCXY.

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