FC: My Workbook: Triangle Study Unit Name: _______________
1: As you complete each part of the workbook, place a check mark in the box to track your progress. | My Progress | Skills Needed Checklist Part I Part II Part III Part IV
2: Solving for the perimeter of a rectangle. Solving for the area of a rectangle. Completing a table of data. Creating an equation based on table data. | Skills Needed | Place a check mark in the boxes next to the skills you feel confident with.
3: Part I Describing Triangles
4: Exploring Triangles!
5: New Vocabulary Vertex/Vertices - the corners of a triangle Base - one side of the triangle, usually the bottom Height - Distance Perpendicular from the base of the triangle to the farthest vertex
6: Describing Triangles | Isosceles Triangle Two sides of the triangle are equal | Triangles can be classified by describing their sides and angles. | Scalene Triangle All sides are different lengths. | Equilateral Triangle All sides are equal.
7: Right Triangle One angle is a right angle | Acute Triangle All angles are less than 90* | Obtuse Triangle One angle is greater than 90* | Equiangular Triangle All angles are equal.
8: Your Turn! How would you describe/classify the following triangles? What do you notice about their sides and angles? Can a triangle fall into more than one classification? | ________________________________________________________________________________________________________ | 3 ft | 5 ft | 4 ft
9: ________________________________________________________________________________________________________________ | 60* 5 m 5 m 60* 60* 5 m | ____________________________________________________________________________________________________________ | 9 in 3 in 3 in
10: Part II Perimeter
11: Perimeter | From our work with rectangles, we know that the perimeter is the distance __________ the figure. We solve for the perimeter by ____________all the _______ together. | Fill in the blanks with the correct word from the word bank. Not all words will be used. perimeter around sides within adding multiplying
12: Equation for Perimeter of a Triangle Use the following triangle to write an equation for the perimeter of a triangle. | P = ___ + ___ + ___ | c a b
13: Your turn! Use the equation you created on the previous page to find the perimeter of the following triangles. | 1. 8m 8m 8m P = _________ | 2. 17ft 29ft 12 ft P = ________
14: Part III Area
15: Solving for Area | Look at the following rectangle. From our previous work, we know that the area of a rectangle is found by multiplying the length by the width. Fill in the equation for finding the area of a rectangle. | H W | Area of a Rectangle: A = ____ x _____
16: Now compare the rectangle to the triangle. Notice that the width of the rectangle can be compared to the base of the triangle, and the height of the rectangle can be compared to the height of the triangle. | L W | h b
17: The __________ of a rectangle is similar to the base of a triangle. The ____________ of a rectangle is similar to the height of a triangle. These terms can be used interchangeably.
18: 15 7.5 35 17.5 20 10
19: Look at the figures to the left. What do you notice about their dimensions? ______________________________________________________________ Now look at the area of each figure, which is printed in black in the middle. Even though the figures of each color have the same dimensions, are the areas the same? How do they compare? _____________________________________________________________________________________________ Use the figures to complete the next two pages.
20: Fill out the table below comparing the area of Triangles and Rectangles with the same dimensions. | T = area of Triangle R = area of Rectangle blue green red | How do the numbers compare?
21: Now, based on the data in your table, create an equation that compares T, the area of a triangle, and R, the area of a rectangle. T = 1/2(R) Remember the equation for the area of a rectangle? ______________ Plug it in for the R in the equation above. Now you have: T = 1/2 (H x W) Now the H will be used to represent the height of the triangle. Replace W with B, because the width of a rectangle is called the base on a triangle. Now you have: T = 1/2 (B x H) This is your final equation!
22: Your turn! Solve for A, the area, of the following right triangles. | 1. A = _______ 8ft 10 ft 2. A = ________ 52 in 60 in
23: Extension: The equation can also be used to solve the area of non-right triangles. Examine the following triangles and identify their base and height. Then solve for the area of the triangle. | B = _____ H = _____ A = _____ B = ______ H = ______ A = ______
24: Part IV Pythagorean Theorem