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Chapter 4: Q10. (page 119)

In the following figure, the two-triangle shown are congruent. Then explain the following statement.

Deduce that DC¯∥AB¯.

Short Answer

Expert verified

HereΔABO≅ΔCDOthusDC¯∥AB¯.

Step by step solution

01

Step 1. Apply the concept of congruent triangles.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped, and turned to be looked identical.

When two lines are cut by a transversal line and if the alternate interior angles are equal then lines are parallel.

02

Step 2. Check the figure.

Consider the figure.

Here the corresponding parts of ΔABO and ΔCDO are congruent such that their corresponding angles and sides are equal such that ∠A=∠Cand ∠B=∠D.

03

Step 3. Step description.

Since when a parallel line is cut by a transversal line then the alternate interior angle is equal thus ∠A=∠C.

This implies that DC¯∥AB¯and ACis a transversal line.

Therefore, this shows that DC¯∥AB¯.

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Most popular questions from this chapter

Suppose you are given a scalene triangle and a point Pon some line localid="1648799479069" l. How many triangles are there with one vertex at localid="1648799462577" P, another vertex on localid="1648799472074" l, and each triangle congruent to the given triangle?

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