Unit 4

Unit 4:

Pythagorean Theorem & Angle Relationships

​Pythagorean Theorem Model

• The area of the two smallest squares will always add up to the area of the biggest square.

• a,b, and c make up the sides of the right triangle that is formed in the center of the diagram.

• In this diagram, the legs of the triangle will always be labeled in regular units and the area will be labeled in units squared.

• a and b are the legs and c is the hypotenuse

• hypotenuse is also known as the diagonal

Multiple Choice

Which statement is true?

• The sum of the areas of square N and square L is equal to the area of square K.

• The sum of the areas of square N and square L is greater than the area of square K.

• The sum of the areas of square N and square K is equal to the area of square L.

• The sum of the areas of square N and square K is less than the area of square L.

​Using Pythagorean Theorem

Multiple Choice

Mickey wants to make a garden with a border in the corner of his yard. He has lumber in several different lengths. Which three lengths could NOT be used to make a right triangle to fit into the corner of his yard?

• 5ft., 3ft., 4 ft.

• 8 ft., 6ft., 10 ft.

• 7 ft., 4 ft., 9 ft.

• 10 ft., 26 ft., 24 ft

Solving For a Missing Side

• Solving for hypotenuse or diagonal: Square your two numbers, add them together, and then take the square root of the sum.

• Solving for a leg (a or b): Square your two numbers, subtract them, and then take the square root of your answer.

• Word problem: Draw a picture, label it & write down important info.

Multiple Choice

Dan secures a ladder against the wall to dust a photo frame mounted on the wall. The foot of the ladder is placed 6 feet from the wall. If the top of the ladder rests 8 feet up the wall, what is the length of the ladder?

• 10 ft

• 5.3 ft

• 12 ft

• 100 ft

Distance Between Points

• When finding the distance between two points on the coordinate grid:

  • Plot the coordinates if not already graphed.

  • Use the diagonal line to draw a right triangle.

  • Count the units on the outside of the triangle to find the legs.

  • Then use formula to calculate the hypotenuse or C.

Multiple Choice

Triangle RST is graphed on the coordinate plane below.

What is the approximate length of segment ST in units?

• 2.8 units

• 4 units

• 6.7 units

• 5.8 units

​Angle Relationships

• All acute (small) angles are congruent (equal)

• All obtuse (big) angles are congruent (equal)

• All angles inside a triangle add up to 180°

• Angle on the outside of a triangle is equal to the sum of the two furthest angles inside of the triangle.

Multiple Choice

Which statement is true?

• The value of x is 75° because the angles shown in the diagram are congruent.

• The value of x is 105° because the angles shown in the diagrams add up to 180°

• The value of x is 140° because the angles shown in the diagrams add up to 360° and 360-(110+110)=140°

• The value of x is 70° because the angles shown in the diagram are both 70°