Q. 4

# Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.

Answer :

△A′BC′ whose sides of the corresponding sides of can be drawn as follows.

Step 1 Draw a △ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = .

Step 2 Draw a ray BX making an acute angle with BC on the opposite side of vertex A.

Step 3 Locate 4 points (as 4 is greater in 3 and 4), B1,B2,B3,B4 on line segment BX.

Step 4 Join B4C and draw a line through B3 , parallel to B4C intersecting BC at C′

Step 5 Draw a line through C' parallel to AC intersecting AB at A'.△A′BC′ is the required triangle.

Justification

∠A=60° (Common)

∠C=∠C'

By AA similarity condition

Also,

AB’=AB ,B’C’=BC and AC’=AC

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