Gr 10 Math Ch 4: Simularity of Triangles

Which condition must be met for two triangles to be considered similar?

They must have the same angles. (correct)

They must have equal areas.

They must be the same size.

They must have proportionate side lengths.

If triangles are similar, what can be deduced about their corresponding sides?

They are all the same size.

They are proportional to one another. (correct)

They are equal in length.

They have a constant ratio that varies with size.

What is the ratio of the sides in a triangle with angles of 30°, 60°, and 90°?

1:2:3

2:1:$rac{1}{2}$

1:$rac{ oot{3}}{2}$:1 (correct)

1:$rac{ oot{2}}{2}$:$rac{3}{2}$

Which of the following statements about the order of vertices in similar triangles is true?

The order must reflect corresponding angles. Signup and view all the answers

In similar triangles $ riangle ABC$ and $ riangle DEF$, what is true about angles A, B, and C?

They are equal to the angles D, E, and F respectively. Signup and view all the answers

What must be true for two triangles to have proportional sides?

They have the same angles. Signup and view all the answers

Which of the following ratios represents the equality in corresponding sides of similar triangles?

$rac{AB}{DE} = rac{BC}{EF}$ Signup and view all the answers

What happens to the ratio of corresponding side lengths if the angle remains constant in similar triangles?

The ratio will remain constant. Signup and view all the answers

Which of the following properties is true for similar triangles?

The ratios of corresponding sides are constant. Signup and view all the answers

In similar triangles, if one pair of sides is proportional, what can be inferred about the other pairs?

Other pairs must also be proportional. Signup and view all the answers

If triangle ABC is similar to triangle DEF, what relationship holds between the angles?

Angle B is equal to angle E. Signup and view all the answers

What is the consequence of not maintaining the correct order of vertices when labeling similar triangles?

The corresponding sides may be incorrectly matched. Signup and view all the answers

Which of the following ratios is consistent for similar triangles with corresponding sides?

$rac{AB}{AC} = rac{DE}{DF}$ Signup and view all the answers

When comparing triangle ABC with triangle GHK, which statement about their corresponding angles is accurate?

Angle A is equal to angle G. Signup and view all the answers

What relationship exists between the areas of similar triangles, such as ABC and DEF?

The area ratio is equal to the square of the side length ratio. Signup and view all the answers

Which of these must be true for triangles to be similar?

They must have two equal angles. Signup and view all the answers

In the context of similar triangles, if triangle ABC is similar to triangle DEF, which of the following must be true?

The ratio of corresponding sides is equal. Signup and view all the answers

Which of the following describes the relationship between the angles of similar triangles?

The corresponding angles are equal. Signup and view all the answers

What does the notation $ \Delta ABC \sim \Delta DEF $ imply about the triangles?

The order of vertices indicates which sides are proportional. Signup and view all the answers

If triangle ABC has side lengths in the ratio 3:4:5, what would be the corresponding sides of a similar triangle DEF with a ratio of 6:8:10?

The sides of triangle DEF are double that of triangle ABC. Signup and view all the answers

Which of the following scenarios correctly demonstrates the properties of similar triangles?

Two triangles with angles of 30°, 60°, and 90° that have identical ratios. Signup and view all the answers

What assumption can be made about the lengths of corresponding sides when comparing two similar triangles?

They will vary but will maintain proportional ratios. Signup and view all the answers

When two triangles are similar, what can be concluded about their corresponding sides and angles?

All corresponding angles are equal and corresponding sides are proportional. Signup and view all the answers

If two triangles have corresponding angles of 45°, 45°, and 90°, which of the following statements is true about their side lengths?

The side lengths will vary but maintain a constant ratio. Signup and view all the answers