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Transcript

Geometry Unit 5 How many different triangles, if any, can be drawn with one 20° angle, one 40° angle, and one 120° angle? a. 0 triangles b. Exactly 1 triangle c. Exactly 2 triangles d. Infinitely many triangles Similar figures - side lengths are proportional, but the angles remain the same. Similar Figures Review 18 ft 10 ft Standard CC.7.G.2. Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Essential Question • How do I know when conditions will form one triangle, no triangle, or more than one triangle? Discovery Try to make triangles using the following colors. Write down if you are able to make a triangle with the colors given. 5 cm, 7 cm, and 10 cm 2 cm, 2 cm, 15 cm 2 2 cm, 5 cm, 12cm 5 cm, 14 cm, and 15 cm 5 cm, 5 cm, and 10 cm Pink, Green, Yellow Dk green, Dk green, Blue Dk green, Pink, Purple Pink, Orange, Blue Pink, Pink, Yellow Yes No No Yes No What can you conclude about the side lengths of triangles? The two SHORTER SIDES must add up to be LONGER than the longest side. Try out your conclusion with other side lengths. You 1) 3) The two SHORTER SIDES must add up Try…to be LONGER than the longest side. 2) 4) Task The two SHORTER SIDES must add up to be LONGER than the longest side. No Yes It must be longer than 2m, but shorter than 18m No No It must be longer than 6 in, but shorter than 34 in Find the range of the third side of each triangle below. Application of the Concept Two miles long each because the two shorter sides must add up to be longer than the longest side and all sides must add up to be 6 miles. It must be longer than 7 feet, but shorter than 17 feet. The two SHORTER SIDES must add up to be LONGER than the longest side. Closing • How do you know when a triangle can be formed when given various side lengths? Any two sides of a triangle will add up to be longer than the other side. • How do you know when and how many triangles can be formed when given three angle measurements? All angles in a triangle must add up to 180°. Triangles with the same angle measurements can have varying side lengths (similar figures). Exploragons Contest 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18