Question 16 of 42intermediate🔍 AnalyzeShort Answer2 marks

ABCD is a parallelogram. P and Q are any two points on side AB. What can you say about the ratio area (ΔPCD): area (ΔQCD)?

Correct Answer

1:1

Exercise: Exercise Set 6.2 | Q: 6 | (Page 25)
For More Understanding

Explanation

Triangles PCD and QCD share the same base CD. Since P and Q are points on side AB of parallelogram ABCD, their perpendicular distances (heights) to the base CD are equal. Triangles with equal bases and equal heights have equal areas, making the ratio 1:1.

Solution Steps

  1. Step 1: Identify that both ΔPCD and ΔQCD share the same base CD.

  2. Step 2: Note that since P and Q are points on side AB of parallelogram ABCD, the perpendicular distance (or height) from both P and Q to the base CD is equal to the distance between the parallel sides AB and CD.

  3. Step 3: Conclude that since Area = 1/2 × base × height, and both the base and height are equal for the two triangles, their areas are equal. Thus, the ratio area (ΔPCD): area (ΔQCD) is 1:1.

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