In this lesson, we will learn how to use the converse of the Pythagorean theorem to determine whether a triangle is a right triangle.

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 π = π + π 2 2 2 is necessarily a right triangle?

Let us assume that β³ π΄ π΅ πΆ is of side lengths π , π , and π , with π = π + π 2 2 2 . Let β³ π· π΅ πΆ be a right triangle of side lengths π , π , and π .

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

We know that for β³ π΄ π΅ πΆ , π = π + π 2 2 2 .

What do you conclude about π ?

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

What do you conclude about β³ π΄ π΅ πΆ ?

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

Is a right triangle at ?

Q7:

Q8:

Q9:

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.

Q10:

Q11:

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

Q12:

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

Q13:

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

Q14:

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

Q15:

Q16:

Q17:

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

Q18:

What does ( π΄ πΆ ) 2 equal to?

Q19:

In the figure shown, suppose that π΄ πΈ = 2 π΅ πΆ and π΅ π· = 8 . Determine π΄ π· and πΈ π· rounded to the nearest hundredth, if necessary.

Q20:

Q21:

π΄ π΅ πΆ is a triangle where π΄ π΅ = 3 c m , π΅ πΆ = 4 c m and π΄ πΆ = 5 c m . Find the size of β π΄ π΅ πΆ .

Q22:

π΄ π΅ πΆ is a triangle where π΄ π΅ = π΄ π΅ = 5 c m , π΅ πΆ = 1 2 c m and π΄ πΆ = 1 3 c m . Find the size of β π΄ π΅ πΆ .

Q23:

Two lines intersect at the point π΄ ( 0 , 1 ) . One line goes through the point π΅ ( 2 , 3 ) , and the other goes through the point πΆ ( 2 , β 1 ) .

Find the lengths of π΄ π΅ , π΄ πΆ , and π΅ πΆ .

Using the Pythagorean theorem, decide: is triangle π΄ π΅ πΆ a right triangle?

Are the two lines perpendicular?

Q24:

Two lines intersect at the point π΄ ( 3 , β 1 ) . One line goes through the point π΅ ( 5 , 1 ) , and the other goes through the point πΆ ( β 2 , 6 ) .

Find the lengths of π΄ π΅ , π΄ πΆ , and π΅ πΆ

Hence, are the two lines perpendicular?

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