Practice Similarity (∼) (5) - Properties of Triangles - IB 10 Mathematics – Group 5, Geometry & Trigonometry

Practice: Similarity (∼)

Lesson 5Properties of Triangles

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9 questions

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6 sample questions

Question 1.
Identify whether the following pairs of triangles are similar. Triangle ABC with angles of 30°, 60°, 90° and Triangle DEF with angles of 30°, 60°, 90°.
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Look for equal angles.
Question 2.
Is it true that if two triangles have two equal angles, their corresponding sides must also be in the same ratio?
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Consider the definition of similar triangles.
3Question 3.
When two triangles are similar, what is true about their angles?
- They are equal
- They are different
- They are the same size
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Consider the definition of similar triangles.
4Question 4.
If two triangles have a corresponding side ratio of 3:5, what can we conclude about their areas?
- In the ratio of 3:5
- In the ratio of 9:25
- Cannot be determined
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Remember: Area is related to the square of the side lengths.
Question 5.
Two triangles have their angles measuring 45°, 45°, and 90°. Triangle XYZ has a hypotenuse of 10 cm. If triangle ABC has a hypotenuse of 5 cm, assess if they are similar and reason out your answer.
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Evaluate the angles and subsequently the ratios.
Question 6.
If triangle DEF has sides measuring 20 cm, 15 cm, and 25 cm, and triangle GHI is similar to triangle DEF with one side measuring 10 cm, find the lengths of the other two sides.
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Use the side ratios to find the remaining sides in triangle GHI.

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