E.1
Have students research various careers in the library that require a knowledge of angles; e.g., surveyors, pilots, meteorologists, architects, cartographers, and carpenters. Reports may include oral presentations, charts, posters, essays, and skits. (COM)
E.2
The sum of the measures of the angles of a triangle is 180°. The first angle is 6 times as large as the second. The third angle is equal to the difference of the other two. What is the measure of the smallest angle? What are the measures of the other two angles?
x + 6x + (6x - x) = 180
E.3. (b)
In pairs, students classify several cut out triangles of varying sizes and shapes. Have them discuss the attributes they used to classify the triangles. Students should also evaluate the classification schemes.
E.4
Devise a game that students can play that involves recognizing the properties of quadrilaterals and other polygons. Create a game card of various geometric shapes consisting of quadrilaterals, triangles, and other polygons. Students work in groups of three: two players and a referee. Each player draws a geometric figure from an envelope containing the cut-up game card pieces. The objective is to guess the opponent's figure correctly before he/she guesses yours by asking a series of alternating questions regarding the properties of the figure. Each question must have a yes or no answer and include only one property. The referee determines if the questions and answers are valid. (CCT)
E.7
Use triangular pieces to form as many polygons as possible. Use the pieces to determine the sum of the measures of the angles of the convex polygons. Care must be taken to ensure that the students recognize that the sum of the angles of all the triangles is actually the sum of the interior angles of the polygon. Some students will deny this; e.g.,
| # of sides | # of diagonals | # of triangles | sum of interior angles |
m. of int. 's of regular polygon
|
m. of ext.'s of regular polygon
| m. of centre angle |
|
3
4 5 6 7 8 9 10 . . . n |
E.11
c ² = a ² + b ²
d ² = e ² + f ²
E.12
Solve each of the following:
1. How far up a wall will a 10 m ladder reach if the base of the ladder is 2 m from the wall?
2. Jason rides his motorcycle at a speed of 80 km/h due south and Jan drives her car at a speed of 100km/h due east. How far apart will they be after 2 hours?
3. Chad uses a guy wire to support a young tree. He attaches it to a point 2 m up the tree trunk. The wire is 3 m long. How far away from the trunk will the wire reach?
E.13
Determine if the corner of a room is a right angle. Devise a plan and carry it out. Reflect back on the reasonableness of the answer.
E.14
Have students draw any right triangle that has acute angles that measure 30° and 60°. Measure and label the angles and sides of the triangle. Display all of their triangles on the board. Have the students compare the various ratios of the sides of the triangles. What conclusions can be made from these results?
E.15
If tan A = 0.4663 then find the m < A.
E.16
1) Calculate m<B
2) Find AB
E.17
Solve each of the following:
1) The angle of elevation from a boat to the top of an iceberg is 75°. If the boat is 200 m from the base of the iceberg how high is the iceberg?
2) A forest ranger in a tower 28 m high sights a fire at an angle of depression of 6°. How far is the fire from the tower?
3) Brent has to look up 70° to see the top of a tree 4 meters away. If his eyes are 1.8 m above the ground, how tall is the tree?