Topics
6. Congruence & Triangles
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Geometry

6.02 Corresponding parts of congruent triangles

Lesson
Practice
Adaptive
Worksheet

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 meters, 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 meters tall, solve for $h$h correct to one decimal place.

Easy
1min

A $4.9$4.9 m high flagpole casts a shadow of $4.5$4.5 m. At the same time, the shadow of a nearby building falls at the same point (S). The shadow cast by the building measures $13.5$13.5 m. Find $h$h, the height of the building, using a proportion statement.

Medium
1min

A school building reaching $h$h meters high casts a shadow of $30$30 m while a $3$3 m high tree casts a shadow of $6$6 m. Solve for $h$h.

Medium
1min
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Outcomes

G.TR.2

The student will, given information in the form of a figure or statement, prove and justify two triangles are congruent using direct and indirect proofs, and solve problems involving measured attributes of congruent triangles.

G.TR.2a

Use definitions, postulates, and theorems (including Side-Side-Side (SSS); Side-Angle-Side (SAS); Angle-Side-Angle (ASA); Angle-Angle-Side (AAS); and Hypotenuse-Leg (HL)) to prove and justify two triangles are congruent.

G.TR.2b

Use algebraic methods to prove that two triangles are congruent.

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