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India
Class X

Applications of Similarity and Symmetry

Lesson
Practice

Interactive practice questions

A stick of height $1.1$1.1 m casts a shadow of length $2.2$2.2 m. At the same time, a tree casts a shadow of $6.2$6.2 m.

The tree that has $h$hm height casts a shadow of $6.2$6.2m long. At the same time, a stick with $1.1$1.1m height casts a shadow of $2.2$2.2m long. When connecting the top of the tree to the tip of its shadow, it forms a right triangle. Also, when connecting the tip of the stick to the tip of its shadow, it forms a right triangle. These two triangles formed are similar due to the side that is represented by the heights of stick and tree correspond to each other. Sides representing the lengths of their shadows are corresponding sides.

 

If the tree has a height of $h$h metres, solve for $h$h.

Easy
1min

A $4.9$4.9 m flagpole casts a shadow of $8.6$8.6 m. Amelia casts a shadow of $2.5$2.5 m.

If Amelia is $h$h metres tall, solve for $h$h correct to one decimal place.

Easy
1min

James is $1.7$1.7 m tall and casts a shadow $2$2 m long. At the same time, a tower casts a shadow $13$13 m long. If the tower is $h$h metres high, solve for $h$h correct to one decimal place.

Easy
1min
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Outcomes

10.G.T.1

Definitions, examples, counterexamples of similar triangles, covering (a) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio, (b) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side, (c) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar, (d) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar (e) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

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