SCALE FACTOR:
Problem: If the following pair of shapes are similar then find out the missing Sides/Angles?
Solution:
We know that –
Final Answer: x = 2 cm
Problem: Find the value of Angle Y and side X?
Solution:
We know that in similar shapes, the corresponding angles are always equal so –
∠Y = 70°
Also-
We Know that –
Final Answer: x = 3 cm and ∠Y = 70°
Problem: Show that the polygon ABCDE is similar to PQRST?
Solution:
The shape of polygon ABCDE is same as that of PQRST, but we need to check the corresponding angles are equal or not. For this we calculate the missing angles of the polygon ABCDE –
As The polygon is a pentagon the sum its angle is 540°. Thus,
As all the corresponding angles of the two polygons came out to be equal we can conclude that they are similar.
Final Answer: x = 135°
Problem: Are the following triangles similar if yes find length scale factor?
Solution:
Yes, because the shape is same and sides are in proportion –
Final Answer: 2 cm
Problem: Are the following triangles similar? Give reason.
Solution:
Yes, the triangles are similar as the corresponding angle equal and the shape is equal also the sides are in proportion –
Final Answer: 2 cm
Problem: Find out the missing sides of the triangle shown in diagram –
Solution:
The Triangles shown in above diagram are similar, because –
According to the interior angle property of parallel lines –
a = e
b = f
Vertically Opposite Angles –
c = d
image
Since the triangles are similar their sides should be in proportion means that –
Final Answer: x = 16 cm and y = 14 cm
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