Pre-Test

Directions: Determine, to 2 decimal

places, the length of the hypotenuse of

the right-angled triangles whose two

shorter sides have the lengths given

below.

1.) 2 cm and 5 cm

2.) 1 cm and 2 cm

3.) 8 cm and 9 cm

4.) 1 cm and 1 cm

5.) 1.73 cm and 1 cm

Where did this come

from???

Over 2,500 years ago, a Greek

mathematician named Pythagoras

popularized the concept that a

relationship exists between the

and the of

and that this relationship is

true for right triangles.

Pythagoras

The Egyptians knew of this concept, as it

related to 3, 4, 5 right triangles, long

before the time of Pythagoras. It was

Pythagoras, however, who generalized the

concept and who is attributed with its

first geometrical demonstration. Thus, it

has become known as the Pythagorean

Theorem.

= the Pythagorean Theorem

“In any right triangle, the square of the length of the

hypotenuse is equal to the sum of the squares of the

lengths of the legs.“

This relationship can be stated as:

For any RIGHT TRIANGLE

𝑎2

+ 𝑏2

= 𝑐2

𝑎2

+ 𝑏2

= 𝑐2

Can you label the triangle?

b

c

a

a, b are legs

c is the hypotenuse

(c is across from the hypotenuse)

leg hypotenuse

leg

Task Card

Group 1

1. Road Trip: Let’s say two friends are

meeting at a playground. Mary is already at

the park but their friend Bob needs to get

there taking the shortest path possible. Bob

has two ways he can go – he can follow the

roads getting to the park – first heading

south 3 miles, then heading west four miles.

The total distance covered following the

roads will be 7 miles. The other way he can

get there is by cutting through some open

fields and walk directly to the park.

Task Card

Group 2

2. Painting on a Wall: Painters use ladders to

paint on high buildings and often use the help

of Pythagorean Theorem to complete their

work. The painter needs to determine how tall

a ladder needs to be in order to safely place

the base away from the wall so it won’t tip

over. In this case the ladder itself will be the

hypotenuse. Take for example a painter who

has to paint a wall which is about 3m high. The

painter has to put the base of the ladder 2m

away from the wall to ensure it won’t tip. What

will be the length of the ladder required by the

painter to complete his work?

Task Card

Group 3

3. What T.V. Size Should You Buy?:

Mr. James saw an advertisement of a

T.V. in the newspaper where it is

mentioned that the T.V. is 16 inches

high and 14 inches wide. Calculate

the diagonal length of its screen for

Mr. James by using Pythagorean

Theorem.

Task Card

Group 4

4. Finding the Right Sized Computer:

Mary wants to get a computer monitor

for her desk which can hold a 22-inch

monitor. She has found a monitor 16

inches wide and 10 inches high. Will

the computer fit into Mary’s cabin?

Post-Test

Directions: Determine, to 2 decimal places, the length

of the hypotenuse of the right-angled triangles whose

two shorter sides have the lengths given below.

1.) 2 cm and 5 cm

2.) 1 cm and 2 cm

3.) 8 cm and 9 cm

4.) 1 cm and 1 cm

5.) 1.73 cm and 1 cm

Post-Test

Directions: Determine, to 2 decimal

places, the length of the hypotenuse of

the right-angled triangles whose two

shorter sides have the lengths given

below.

1.) 2 cm and 5 cm

2.) 1 cm and 2 cm

3.) 8 cm and 9 cm

4.) 1 cm and 1 cm

5.) 1.73 cm and 1 cm