NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.2 – Part 4

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Corresponding Angles

Hear m and n two parallel line ,∠1 = ∠5,∠2 = ∠6,∠4 =∠8,∠3 = ∠6

Hear M and N Two Parallel Line

Hear m and n two parallel line ,∠1 = ∠5,∠2 = ∠6,∠4 =∠8,∠3 = ∠6

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Corresponding Angle:-the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Q-7 ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that

  1. D is the mid-point of AC

Solution:

ABC Is a Triangle

ABC is a triangle is the midpoint of AB and MM||BC and D is the midpoint of AC

Give triangle of ABC at C, a line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D.

  1. In ,

    • M is the midpoint of AB and

    • Thus; D is the midpoint of AC (Converse of mid-point theorem)

  2. (Corresponding angles)

    • Also,

    • Thus, and

  3. In and ,

  • (D is the midpoint of side AC)

  • (Each 90°)

  • (Common)

  • Thus, by Side-Angle-Side congruence condition.

  • by Corresponding Part of Congruent Triangles

  • also, (M is mid-point of AB)

  • Hence,