Gr12 Mathematics: Ch 7.5 Pythagorean Theorem

What is the Pythagorean Theorem a fundamental principle of?

Algebra

Trigonometry

Calculus

Geometry (correct)

In the Pythagorean Theorem, what is the angle of the given triangle?

45°

60°

120°

90° (correct)

What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?

To prove the theorem

To find the area of the triangle

To find the sum of the squares

To form similar triangles (correct)

What is the criterion used to show that ∆ABD is similar to ∆CBA?

AAA similarity criterion Signup and view all the answers

What is the formula for the area of a triangle?

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

What is the converse of the Pythagorean Theorem?

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled. Signup and view all the answers

What is true about triangles with equal heights?

They have proportional areas to their bases Signup and view all the answers

What is true about triangles with equal bases between the same parallel lines?

They have equal areas Signup and view all the answers

What is the relationship between the square on the hypotenuse and the squares on the other two sides in a right-angled triangle?

The square on the hypotenuse is equal to the sum of the squares on the other two sides Signup and view all the answers

What is the purpose of constructing ∆CAD and ∆ABD in the proof of the Pythagorean Theorem?

To prove that ∆CAD is similar to ∆ABD Signup and view all the answers

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, what can be concluded?

The angle included by the other two sides is a right angle Signup and view all the answers

What is the relationship between the areas of triangles with equal heights?

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

What is true about the similarity of ∆CAD and ∆CBA in the proof of the Pythagorean Theorem?

They are similar triangles by AAA similarity criterion Signup and view all the answers

What is the formula for the area of a triangle, given the base and height?

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

What can be concluded if ∆ABC is a right-angled triangle and AC^2 = AB × BC?

AC is the hypotenuse of the triangle Signup and view all the answers

What is the relationship between the areas of triangles with equal bases between the same parallel lines?

They are equal in area Signup and view all the answers

What is the significance of ∠A1 = ∠C in the proof of the Pythagorean Theorem?

It shows that ∆CAD is similar to ∆CBA Signup and view all the answers

What is the purpose of adding the results in steps 3 and 4 of the proof?

To prove that BC^2 = AB^2 + AC^2 Signup and view all the answers

What is the implication of the converse of the Pythagorean Theorem?

If the square of one side is equal to the sum of the squares of the other two sides, then the angle included by these two sides is a right angle Signup and view all the answers

What is the reason for constructing ∆CAD and ∆ABD in the proof?

To establish the similarity between ∆CAD and ∆CBA, and ∆ABD and ∆CBA Signup and view all the answers

What can be concluded about ∆ABC if AC^2 = AB × BC?

The triangle is right-angled Signup and view all the answers

What is the relationship between the areas of ∆CAD and ∆CBA?

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

What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?

To construct ∆CAD and ∆ABD, which are similar to ∆CBA Signup and view all the answers

What is the significance of BC^2 = BD × BC + CB × DC in the proof?

It proves that the square of one side is equal to the sum of the squares of the other two sides Signup and view all the answers

Gr12 Mathematics: Ch 7.5 Pythagorean Theorem

Questions and Answers

What is the Pythagorean Theorem a fundamental principle of?

In the Pythagorean Theorem, what is the angle of the given triangle?

What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?

What is the criterion used to show that ∆ABD is similar to ∆CBA?

What is the formula for the area of a triangle?

What is the converse of the Pythagorean Theorem?

What is true about triangles with equal heights?

What is true about triangles with equal bases between the same parallel lines?

What is the relationship between the square on the hypotenuse and the squares on the other two sides in a right-angled triangle?

What is the purpose of constructing ∆CAD and ∆ABD in the proof of the Pythagorean Theorem?

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, what can be concluded?

What is the relationship between the areas of triangles with equal heights?

What is true about the similarity of ∆CAD and ∆CBA in the proof of the Pythagorean Theorem?

What is the formula for the area of a triangle, given the base and height?

What can be concluded if ∆ABC is a right-angled triangle and AC^2 = AB × BC?

What is the relationship between the areas of triangles with equal bases between the same parallel lines?

What is the significance of ∠A1 = ∠C in the proof of the Pythagorean Theorem?

What is the purpose of adding the results in steps 3 and 4 of the proof?

What is the implication of the converse of the Pythagorean Theorem?

What is the reason for constructing ∆CAD and ∆ABD in the proof?

What can be concluded about ∆ABC if AC^2 = AB × BC?

What is the relationship between the areas of ∆CAD and ∆CBA?

What is the purpose of drawing AD ⊥ BC in the proof of the Pythagorean Theorem?

What is the significance of BC^2 = BD × BC + CB × DC in the proof?

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