Question

Draw a ΔABC in which AB = 5cm, BC = 6cm and angle ABC = 60°. Construct a triangle similar to ABC with scale factor 5/7. Justify the construction.

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Answer 1

Answer:

Step of Construction

1. draw a line segment An = 5cm.

2. From points B, draw angle ABY = 60° on which BC = 6cm.

3. Join AC, ΔABC is the required Δ.

4. From A draw any ray AX downward making an acute angle.

5. Mark 7 points B1, B2, B3, B4, B5, B6, & B7 on AX, such that AB1 = B1B2 = B2B3 = B3B4 = B4B5 = B5B6 = B6B7.

6. Join B7B and from B5 draw B5M || B7B intersecting AB at M.

7. From point M draw MN || BC intersecting AC at N. Then, ΔAMN is the required triangle whose sides are equal to 5/7 of the corresponding sides of the ΔABC.

Justification

Here, B5M || B7B. (by construction)

AM/MB = 5/2

Now, AB/AM = AM + MB/AM

= 1 + MB/AM = 1+2/5 = 7/5

Also, MN || BC

ΔAMN ~ ΔABC

TTherefore, AM/AB = AN/AC = NM/BC = 5/7