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# Worksheet: The Converse of the Pythagorean Theorem

Q1:

The Pythagorean theorem states that, in a right triangle, the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. Does this mean that a triangle where is necessarily a right triangle?

Let us assume that is of side lengths , , and , with . Let be a right triangle of side lengths , , and .

Using the Pythagorean theorem, what can you say about the relationship between , , and ?

• A
• B
• C

We know that for , .

What do you conclude about ?

• A
• B
• C

Is it possible to construct different triangles with the same length sides?

• Ayes
• Bno

What do you conclude about ?

• AIt is congruent to , so it has a right angle at .
• BIt is congruent to , so it has a right angle at .
• CIt is similar to , so it has a right angle at .
• DIt is similar to , so it has a right angle at .
• EIt is congruent to , so it has a right angle at .

Q2:

What can the converse of the Pythagorean theorem be used for?

• Afinding the angles in a triangle
• Bfinding lengths in an equilateral triangle
• Cdemonstrating that a triangle is equilateral
• Ddemonstrating that a triangle has a right angle
• Edemonstrating that a triangle is an isosceles triangle

Q3:

Can the lengths 7.9 cm, 8.1 cm, and 5.3 cm form a right triangle?

• Ano
• Byes

Q4:

Can the lengths 16.6 cm, 6.3 cm, and 11.3 cm form a right triangle?

• Ano
• Byes

Q5:

Can the lengths 14.4 cm, 19.2 cm, and 24 cm form a right triangle?

• Ayes
• Bno

Q6:

Is a right triangle at ?

• Ano
• Byes

Q7:

Is a right triangle at ?

• Ayes
• Bno

Q8:

Is a right triangle at ?

• Ano
• Byes

Q9:

A triangle has sides of lengths 36.4, 27.3 and 45.5. What is its area?

Q10:

A triangle has sides of lengths 20.4, 59.5 and 62.9. What is its area?

Q11:

A triangle has sides of lengths 44, 4.2 and 44.2. What is its area?

Q12:

In triangle , is perpendicular to , lies between and , , , and . Is a right triangle?

• Ayes
• Bno

Q13:

What does equal to?

• A
• B
• C
• D

Q14:

In triangle point lies on and , , , and . Find the length of to the nearest tenth, and then determine whether is a right triangle or not.

• A , a right triangle
• B , not a right triangle
• C , a right triangle
• D , not a right triangle

Q15:

In triangle point lies on and , , , and . Find the length of to the nearest tenth, and then determine whether is a right triangle or not.

• A , a right triangle
• B , not a right triangle
• C , not a right triangle
• D , a right triangle

Q16:

Two lines intersect at the point . One line goes through the point , and the other goes through the point .

Find the lengths of , , and .

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Using the Pythagorean theorem, decide: is triangle a right triangle?

• AYes
• BNo

Are the two lines perpendicular?

• ANo
• BYes

Q17:

In triangle , let on be the foot of the altitude from . If , , and , is right triangle at ?

• Ano
• Byes

Q18:

In triangle , let on be the foot of the altitude from . If , , and , is right triangle at ?

• Ayes
• Bno

Q19:

In triangle , let on be the foot of the altitude from . If , , and , is right triangle at ?

• Ano
• Byes

Q20:

Two lines intersect at the point . One line goes through the point , and the other goes through the point .

Find the lengths of , , and .

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

According to the Pythagorean theorem, is triangle a right triangle?

• ANo
• BYes

Hence, are the two lines perpendicular?

• AYes
• BNo

Q21:

is a triangle where , and . Find the size of .

Q22:

In the figure shown, suppose that and . Determine and rounded to the nearest hundredth, if necessary.

• A ,
• B ,
• C ,
• D ,

Q23:

is a triangle where , and . Find the size of .

Q24:

Is a right triangle at ?

• Ano
• Byes