d. Using your information from the chart above, fill-in the statement below.
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1 STATION #1: Sum of the Angles in a Triangle Complete the following tasks for station 1. a. Form two different triangles using the Anglegs provided. b. Find the measures of the three angles in the two triangles you formed. Record your measurements in the chart below. c. Find the sum of the three angles you measured. Record your sum in the chart below TRIANGLE ANGLE 1 ANGLE 2 ANGLE 3 SUM OF THREE ANGLES 1 2 d. Using your information from the chart above, fill-in the statement below. SUM OF THE ANGLES OF A TRIANGLE= e. Check your results with your teacher before completing examples 1 and 2. EXAMPLES: 1. Find the value of x and the measures of each angle. 2. The variable expressions represent the angle measures of a triangle. Find the measure of each angle. BEFORE MOVING ON, CHECK YOUR ANSWERS TO EXAMPLES #1-2 POSTED IN THE FRONT OF
2 EXPLORATION #2: Forming a Triangle Complete the following tasks for station 2. a. Try to form triangles with each of the given Angleg colors. Complete the table below. Short Side Middle Side Long Side Do the three sides form a triangle? Yellow (10cm) Pink (5cm) Pink (5cm) Teal (2.5cm) Orange (14.14cm) Red (8.66cm) Green (7.07cm) Red (8.66cm) Blue (15cm) Blue (15cm) Yellow (10cm) Purple (12.24cm) Sum of the short and middle sides Is the sum of the short and middle sides <, >, or = to the longest side? (Write <, >, or = to in the box below.) b. Check your table results with your teacher before completing part c. c. Highlight the rows that form triangles. What do you notice about the sum of the short and middle sides compared to the longest side? Fill-in the statement below. SUM OF THE SHORT AND MIDDLE SIDES LONG SIDE d. Check your results with your teacher before completing examples 3-5. EXAMPLES: Use the relationship from part c in the statement above to prove whether the three given side lengths form a triangle. Show your work to justify your answer. 3. 2, 2, , 7, , 2, 5 BEFORE MOVING ON, CHECK YOUR ANSWERS TO EXAMPLES #3-5 POSTED IN THE FRONT OF
3 EXPLORATION #2: Triangle Inequalities in One Triangle a. Measure and label the unknown side lengths/angles in the triangles below. b. Look at the position of your smallest angle and your shortest side. Are they adjacent (next to) or opposite (across) from each other? Triangle #1 Triangle #2 c. Look at the position of your middle angle and middle side. Are they adjacent (next to) or opposite (across) from each other? Triangle #1 Triangle #2 d. Look at the position of your largest angle and longest side. Are they adjacent (next to) or opposite (across) from each other? Triangle #1 Triangle #2 e. Using your results from above, fill in the statements below that summarizes how the positions of side lengths are related to positions of angles in ONE triangle. The SMALLEST angle is the SHORTEST side. The angle is the MIDDLE side. The LARGEST angle is the side. d. Check your results with your teacher before completing examples 6-7. EXAMPLES: Write the measurements (sides and angles) of the triangles in order from least to greatest BEFORE MOVING ON, CHECK YOUR ANSWERS TO EXAMPLES #6-7 POSTED IN THE FRONT OF
4 EXPLORATION #3: Hinge Theorem (Inequalities within two triangles) 1. Connect the yellow and green Anglegs together at a 120 angle. Find the Angleg that completes the triangle. Draw a sketch of the triangle below. 2. Using another set of yellow and green Anglegs, connect them together at a 120 angle. Find the Angleg that completes the triangle. Draw a sketch of the triangle below. 3. Compare the lengths of the Anglegs used to complete the triangles. Which length was larger and why? 4. Use your answers for question 3 to finish the following HINGE THEOREM (stated two ways) (Use for examples 8 12) Given the angle measure, compare the lengths of third side. Given the side length, compare the measure of the angle. EXAMPLES: Find the range of possible values for each variable
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2.0 Trigonometry Review Date: Key Ideas: The three angles in a triangle sum to. Pythagorean Theorem: where c is always the. In trigonometry problems, all vertices (corners or angles) of the triangle are