Lesson 1.5 Triangles PDF

# 1.5 Triangles ## Museum of Modern Art, Bonn, Germany The image is of three tall blue cone-shaped towers or structures. They have a glass roof and are covered in blue tiles. They are in a garden setting with some landscaping and a flat roof. The image has a caption below. ## Triangles A tri...

# 1.5 Triangles ## Museum of Modern Art, Bonn, Germany The image is of three tall blue cone-shaped towers or structures. They have a glass roof and are covered in blue tiles. They are in a garden setting with some landscaping and a flat roof. The image has a caption below. ## Triangles A triangle is a shape with three angles and three sides. Triangles can be classified by the lengths of their sides or by the measures of their angles. In Activity 8, you will discover and define these classifications. ## Activity 8 - Classifying triangles A triangle can be classified as an acute triangle, an obtuse triangle or a right-angled triangle (also sometimes called a right triangle). Look at the triangles below and answer the questions that follow. | Type | Image | |------------|:-----------------------------------------------------------------------------------------------------------------------------| | Acute | Six triangles labeled with different angles ranging from 40° to 80°. | | Obtuse | Five triangles labeled with different angles ranging from 25° to 130°. | | Right-angled | One triangle labeled with angles of 30°, 60° and 90°. | 1. How would you define each of the following? * an acute triangle * an obtuse triangle * a right-angled triangle 2. Can a triangle be two of those classifications at the same time? Explain. ## Investigation 3 - Interior angles of a triangle You can perform the following investigation using paper and pencil or with dynamic geometry software. For example, go to mathsisfun.com/geometry/protractor-using.html, and scroll down to 'Have a Go Yourself'. 1. Using a ruler, draw six different triangles. Use the angles listed in the table below for the first three triangles. Draw the other three triangles as you wish. 2. Use a protractor to measure the unknown angle(s) in each triangle. Write down your measurements in a table like the one below. | Triangle | 1st angle | 2nd angle | 3rd angle | | -------- | --------- | --------- | --------- | | 1 | 40° | 80° | | | 2 | 90° | 60° | | | 3 | 50° | 70° | | | 4 | | | | | 5 | | | | | 6 | | | | 3. What pattern do you see related to the measures of the angles in each triangle? 4. Draw a few other triangles and test your theory for other cases. 5. Write down what you found as a general rule. ## ATL1 6. Cut out one of the triangles and fold the angles inward so that the vertices all touch each other but don't overlap. What does that show? 7. Cut out another triangle and rip off the corners. Explain how you could demonstrate your rule with these corners. ## Reflect and discuss 9 * Can a right-angled triangle also be an obtuse triangle? Explain. * An exterior angle of a triangle is an angle outside of the triangle, as shown here. How does the measure of this angle relate to the measures of the two interior angles (A and B) that are not next to it? *The image shows a triangle with an exterior angle marked and labeled. * * How does the sum of the angles inside a triangle relate to the sum of the angles inside a rectangle? Explain. ## Example 3 **Q** Determine the measure of the unknown angles. *The image shows a triangle with labeled angles.* **A** *Angles on a line add up to 180°. This means that angle _DCA_ is 138°.* * The sum of the interior angles of a triangle is 180°. If you know the measures of two of the angles of a triangle, you can calculate the measure of the third. * angle _BCA_ is 42°. * angle _BAC_ is 58°.*