Unit 10 Toolbox

A Theorem is a conjecture that has been proven true. One of the most well known Theorems in mathematics in the Pythagorean Theorem named for Pythagoras(570 BCE to 495 BCE) who was a Greek mathematician and philosopher.

https://www.britannica.com/biography/Pythagoras

Pythagorean Theorem: In a right triangle, the sum of the squares of the legs equals the hypotenuse squared.

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Draw a right triangle, label the hypotenuse c and the legs a and b. Write the theorem as an equation using a, b and c.

There are well more than 371 Pythagorean theorem proofs. A 12-year old Einstein, Leonardo da Vinci and James A. Garfield have written proofs for this theorem. There is also evidence that Pythagorean Theorem was proven by Babylonian mathematicians 1,000 years before Pythagoras was born.

Can you see why this theorem may be referred to as the Theorem of the Three Squares after viewing the image below? The sum of the areas of the red and green squares is equal to the area of the blue square.

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Pythagorean Triples are whole number side lengths of right triangles. Choose all Pythagorean Triples from the list below.

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The converse of the Pythagorean Theorem is also true. Choose the converse from the choices below.
Remember: The converse of If a, then b is If b, then a.

If a² + b² = c², then the triangle is a right triangle.

If a² + c² = b², then the triangle is a right triangle.

If a²+ b² = c², then the triangle is an acute triangle.

If the triangle is a right triangle, then a²+ b² = c².

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If c² > a² + b², then the triangle is. . .

acute

right

obtuse

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If c² < a² + b², then the triangle is. . .

acute

right

obtuse

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Choose the correct ratio of side lengths in an isosceles right triangle (45-45-90), then label the triangle with the labels used in the ratio in the Show Your Work section.

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Choose the correct ratio of side lengths in a 30-60-90 triangle, then label the triangle with the labels used in the ratio in the Show Your Work section.

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Which is the correct distance formula if given the points

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Unit 10 Toolbox

Draw a right triangle, label the hypotenuse c and the legs a and b. Write the theorem as an equation using a, b and c.

Pythagorean Triples are whole number side lengths of right triangles. Choose all Pythagorean Triples from the list below.

The converse of the Pythagorean Theorem is also true. Choose the converse from the choices below.
Remember: The converse of If a, then b is If b, then a.

If c² > a² + b², then the triangle is. . .

If c² < a² + b², then the triangle is. . .

Choose the correct ratio of side lengths in an isosceles right triangle (45-45-90), then label the triangle with the labels used in the ratio in the Show Your Work section.

Choose the correct ratio of side lengths in a 30-60-90 triangle, then label the triangle with the labels used in the ratio in the Show Your Work section.

Which is the correct distance formula if given the points

Which is the correct circle equation if given the radius, r, a point on the circle (x, y) and the center(h, k)?

Draw a right triangle, label the hypotenuse c and the legs a and b. Write the theorem as an equation using a, b and c.

Pythagorean Triples are whole number side lengths of right triangles. Choose all Pythagorean Triples from the list below.

The converse of the Pythagorean Theorem is also true. Choose the converse from the choices below.
Remember: The converse of If a, then b is If b, then a.

If c² > a² + b², then the triangle is. . .

If c² < a² + b², then the triangle is. . .

Choose the correct ratio of side lengths in an isosceles right triangle (45-45-90), then label the triangle with the labels used in the ratio in the Show Your Work section.

Choose the correct ratio of side lengths in a 30-60-90 triangle, then label the triangle with the labels used in the ratio in the Show Your Work section.

Which is the correct distance formula if given the points

Which is the correct circle equation if given the radius, r, a point on the circle (x, y) and the center(h, k)?

Unit 10 Toolbox

Unit 10 Toolbox

Draw a right triangle, label the hypotenuse c and the legs a and b. Write the theorem as an equation using a, b and c.

Pythagorean Triples are whole number side lengths of right triangles. Choose all Pythagorean Triples from the list below.

The converse of the Pythagorean Theorem is also true. Choose the converse from the choices below.Remember: The converse of If a, then b is If b, then a.

If c2 > a2 + b2, then the triangle is. . .

If c2 < a2 + b2, then the triangle is. . .

Choose the correct ratio of side lengths in an isosceles right triangle (45-45-90), then label the triangle with the labels used in the ratio in the Show Your Work section.

Choose the correct ratio of side lengths in a 30-60-90 triangle, then label the triangle with the labels used in the ratio in the Show Your Work section.

Which is the correct distance formula if given the points

Which is the correct circle equation if given the radius, r, a point on the circle (x, y) and the center(h, k)?

Draw a right triangle, label the hypotenuse c and the legs a and b. Write the theorem as an equation using a, b and c.

Pythagorean Triples are whole number side lengths of right triangles. Choose all Pythagorean Triples from the list below.

The converse of the Pythagorean Theorem is also true. Choose the converse from the choices below.Remember: The converse of If a, then b is If b, then a.

If c2 > a2 + b2, then the triangle is. . .

If c2 < a2 + b2, then the triangle is. . .

Choose the correct ratio of side lengths in an isosceles right triangle (45-45-90), then label the triangle with the labels used in the ratio in the Show Your Work section.

Choose the correct ratio of side lengths in a 30-60-90 triangle, then label the triangle with the labels used in the ratio in the Show Your Work section.

Which is the correct distance formula if given the points

Which is the correct circle equation if given the radius, r, a point on the circle (x, y) and the center(h, k)?

The converse of the Pythagorean Theorem is also true. Choose the converse from the choices below.
Remember: The converse of If a, then b is If b, then a.

If c² > a² + b², then the triangle is. . .

If c² < a² + b², then the triangle is. . .

The converse of the Pythagorean Theorem is also true. Choose the converse from the choices below.
Remember: The converse of If a, then b is If b, then a.

If c² > a² + b², then the triangle is. . .

If c² < a² + b², then the triangle is. . .