Question

An Architecture firm in Gurgaon, got a project to develop a beautiful resort on a
piece of land in the shape of an isosceles trapezium they divided it in four parts as shown
below:​

Answer 1

Answer:

1.  a) garden & pool

2. c) AAA

3. c) 1 : 1

4. b) 100 : 9

5. b) two

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Answer 2

Answer:

c) Garden and Pool

c) AAA

c) 1:1

c) 50:27

a) one

Step-by-step explanation:

• c) The area of the Garden and Pool are equal because they both are forming congruent triangles ADC and BCD, by the SSS congruency rule.

PROOF:

Side AD = BC, (Sides of Isosceles triangle)

side BD = AC(diagonals of isosceles triangles)

side DC = CD (common))

• c) For proving the similarity of triangles AOB, and COD, the criteria AAA can be used since the angles are equal.

PROOF:

∠AOB = ∠COD (vertically opposite angles)

∠ABO = ∠CDO (interior opposite angles of parallel lines AB and CD and transversal BD)

∠BAO = ∠DCO (interior opposite angles of parallel lines AB and CD and transversal CA)

• c) Area of triangle AOD: triangle BOC = 1:1 since both are congruent.

• c) Area of triangle AOB: Area of COD = 50:27, since, the opposite sides are 360 and 108, and the triangle AOB is bigger than COD.

• a) There is one pair of similar triangles, AOB and COD.