Gr12 Mathematics: Ch 7.3 Triangles

What is the conclusion of triangles with the same height?

Triangles with equal heights have areas proportional to their heights.

Triangles with equal heights have bases proportional to their areas.

Triangles with equal heights have areas equal to each other.

Triangles with equal heights have areas proportional to their bases. (correct)

What is the formula to find the area of triangle ABC?

Area = BC * h

Area = (1/3) * BC * h

Area = BC / h

Area = (1/2) * BC * h (correct)

What can be concluded about two triangles on the same base and equal in area?

The triangles are congruent.

The triangles lie between parallel lines. (correct)

The triangles have equal heights.

The triangles have equal perimeters.

What is the statement of the Proportion Theorem?

A line drawn parallel to one side of a triangle divides the other two sides of the triangle in the same proportion. Signup and view all the answers

What is the formula of the Proportion Theorem?

AD/DB = AE/EC Signup and view all the answers

What is the statement of the Mid-point Theorem?

The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to half the length of the third side. Signup and view all the answers

What can be concluded about triangles with the same base and between the same parallel lines?

The triangles have equal areas. Signup and view all the answers

What is the purpose of drawing perpendiculars in the proof of the Proportion Theorem?

To show that the line divides the sides proportionally. Signup and view all the answers

What is the condition for the Mid-point Theorem to be applied?

If the line joining the midpoints of two sides of a triangle is parallel to the third side Signup and view all the answers

What is the formula to find the area of a triangle?

Area = (1/2) × base × height Signup and view all the answers

What can be said about the areas of two triangles with equal heights?

They are proportional to their bases Signup and view all the answers

What is the condition for two triangles to be similar?

If they are equiangular Signup and view all the answers

What is the Proportion Theorem?

A line drawn parallel to one side of a triangle divides the other two sides proportionally Signup and view all the answers

What is the converse of the Mid-point Theorem?

The line drawn from the midpoint of one side of a triangle parallel to another side bisects the third side of the triangle Signup and view all the answers

If DE is parallel to BC and AD = 4, what is the length of DB?

6 Signup and view all the answers

In a triangle, if the line joining the midpoints of two sides is drawn, what can be said about the line?

It is parallel to the third side and half its length. Signup and view all the answers

What is the ratio of the areas of two triangles with equal heights?

Directly proportional to the bases Signup and view all the answers

If two triangles are equiangular, what can be said about the corresponding sides?

They are proportional Signup and view all the answers

What is the converse of the Mid-point Theorem?

The line drawn from the midpoint of one side of a triangle bisects the third side. Signup and view all the answers

If two triangles have proportional corresponding sides, what can be said about the triangles?

They are similar Signup and view all the answers

What can be said about the heights of two triangles on the same base and equal in area?

They are equal. Signup and view all the answers

If a line is drawn parallel to one side of a triangle, what can be said about the other two sides?

They are divided in the same ratio. Signup and view all the answers

What is the ratio of the areas of two triangles with equal heights and bases in the ratio of 2:3?

2:3 Signup and view all the answers

If two triangles have areas in the ratio of 2:3 and their heights are equal, what can be said about their bases?

Their bases are in the ratio of 2:3. Signup and view all the answers

What is the length of the line joining the midpoints of two sides of a triangle?

Half the length of the third side. Signup and view all the answers

What can be said about the areas of two triangles with the same base and between the same parallel lines?

They are equal. Signup and view all the answers

If two triangles have equal areas and their bases are in the ratio of 2:3, what can be said about their heights?

Their heights are in the ratio of 3:2. Signup and view all the answers

What is the purpose of drawing perpendiculars in the proof of the Proportion Theorem?

To show that the line divides the sides proportionally. Signup and view all the answers

What can be concluded about two triangles with proportional areas and equal heights?

They have proportional bases. Signup and view all the answers

In the proof of the Proportion Theorem, why are perpendiculars drawn from E to AD and from D to AE?

To show that the line divides the sides proportionally. Signup and view all the answers

If two triangles have equal areas and their bases are in the ratio of 2:3, what can be said about their heights?

Their heights are in the ratio of 3:2. Signup and view all the answers

What is the condition for two triangles to have areas in a certain ratio?

They should have proportional corresponding sides. Signup and view all the answers

What can be concluded about a line drawn parallel to one side of a triangle?

It divides the other two sides in the same proportion. Signup and view all the answers

If two triangles have proportional corresponding sides, what can be said about their areas?

They are in a certain ratio. Signup and view all the answers

What is the ratio of the areas of two triangles with equal heights and bases in the ratio of 2:3?

2:3 Signup and view all the answers

What can be said about the heights of two triangles on the same base and equal in area?

They are equal. Signup and view all the answers

If two triangles have proportional corresponding sides and one of them has a side of length 6 units, what can be said about the corresponding side in the other triangle?

It is greater than 6 units Signup and view all the answers

If a line is drawn parallel to one side of a triangle and intersects the other two sides, what can be said about the line segments formed?

They are proportional to the original sides Signup and view all the answers

If two triangles have equal areas and their heights are in the ratio of 2:3, what can be said about their bases?

They are in the ratio of 3:2 Signup and view all the answers

If a line is drawn through the midpoint of one side of a triangle, what can be said about the line and the third side of the triangle?

The line is parallel to the third side and half its length Signup and view all the answers

If two triangles have bases in the ratio of 2:3 and their areas are equal, what can be said about their heights?

They are equal Signup and view all the answers

Gr12 Mathematics: Ch 7.3 Triangles

Questions and Answers

What is the conclusion of triangles with the same height?

What is the formula to find the area of triangle ABC?

What can be concluded about two triangles on the same base and equal in area?

What is the statement of the Proportion Theorem?

What is the formula of the Proportion Theorem?

What is the statement of the Mid-point Theorem?

What can be concluded about triangles with the same base and between the same parallel lines?

What is the purpose of drawing perpendiculars in the proof of the Proportion Theorem?

What is the condition for the Mid-point Theorem to be applied?

What is the formula to find the area of a triangle?

What can be said about the areas of two triangles with equal heights?

What is the condition for two triangles to be similar?

What is the Proportion Theorem?

What is the converse of the Mid-point Theorem?

If DE is parallel to BC and AD = 4, what is the length of DB?

In a triangle, if the line joining the midpoints of two sides is drawn, what can be said about the line?

What is the ratio of the areas of two triangles with equal heights?

If two triangles are equiangular, what can be said about the corresponding sides?

What is the converse of the Mid-point Theorem?

If two triangles have proportional corresponding sides, what can be said about the triangles?

What can be said about the heights of two triangles on the same base and equal in area?

If a line is drawn parallel to one side of a triangle, what can be said about the other two sides?

What is the ratio of the areas of two triangles with equal heights and bases in the ratio of 2:3?

If two triangles have areas in the ratio of 2:3 and their heights are equal, what can be said about their bases?

What is the length of the line joining the midpoints of two sides of a triangle?

What can be said about the areas of two triangles with the same base and between the same parallel lines?

If two triangles have equal areas and their bases are in the ratio of 2:3, what can be said about their heights?

What is the purpose of drawing perpendiculars in the proof of the Proportion Theorem?

What can be concluded about two triangles with proportional areas and equal heights?

In the proof of the Proportion Theorem, why are perpendiculars drawn from E to AD and from D to AE?

If two triangles have equal areas and their bases are in the ratio of 2:3, what can be said about their heights?

What is the condition for two triangles to have areas in a certain ratio?

What can be concluded about a line drawn parallel to one side of a triangle?

If two triangles have proportional corresponding sides, what can be said about their areas?

What is the ratio of the areas of two triangles with equal heights and bases in the ratio of 2:3?

What can be said about the heights of two triangles on the same base and equal in area?

If two triangles have proportional corresponding sides and one of them has a side of length 6 units, what can be said about the corresponding side in the other triangle?

If a line is drawn parallel to one side of a triangle and intersects the other two sides, what can be said about the line segments formed?

If two triangles have equal areas and their heights are in the ratio of 2:3, what can be said about their bases?

If a line is drawn through the midpoint of one side of a triangle, what can be said about the line and the third side of the triangle?

If two triangles have bases in the ratio of 2:3 and their areas are equal, what can be said about their heights?

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