7th Grade Drawing Geometric Figures 20170228 www.njctl.org
Table of Contents Click on a topic to go to that section Determining if a Triangle is Possible Geometric Constructions: The Basics Constructions are shown within Glossary the lesson using paper and Teacher Notes pencil. There are also video links showing how to do the constructions using Geometer's Videos Using Geometer's Sketchpad Sketchpad. A free version of this Video: Constructing Circles program is available at: Video: Constructing Isosceles Triangles http://info.mheducation.com/ sketchpad.trial.html Video: Constructing Equilateral Triangles Video: Congruent Triangles
Determining if a Triangle is Possible Return to Table of Contents
Drawing Triangles How many different acute triangles can you draw? Recall that triangles can be classified according to their side lengths and the measure of their angles. Sides: Scalene no sides are congruent Isosceles two sides are congruent Equilateral all three sides are congruent Angles: Acute all three angles are acute Right contains one right angle Obtuse contains one obtuse angle
Drawing Triangles How many different right scalene triangles can you draw? Recall that triangles can be classified according to their side lengths and the measure of their angles. Sides: Scalene no sides are congruent Isosceles two sides are congruent Equilateral all three sides are congruent Angles: Acute all three angles are acute Right contains one right angle Obtuse contains one obtuse angle
Triangle Inequality Property There is another property that applies to triangles: Click the lab below to learn about the Triangle Inequality Property. Triangle Inequality Lab
Triangle Inequality Property Triangle Inequality : The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What does this mean? If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. If that is not true, then it is not possible to construct a triangle with the given slide lengths.
Example Determine if sides of length 5 cm, 8 cm and 12 cm can form a triangle? Test all three pairs to see if the sum is greater: 5 + 8 > 12 5 + 12 > 8 8 + 12 > 5 13 > 12 17 > 8 20 > 5 Yes, it is possible to construct a triangle with sides of lengths 5 cm, 8 cm and 12 cm.
Example Determine if sides of length 3 ft, 4 ft and 9 ft can form a triangle? Test all three pairs to see if the sum is greater: 3 + 4 > 9 3 + 9 > 4 4 + 9 > 3 7 > 9 12 > 4 13 > 3 No, it is not possible to construct a triangle with sides of lengths 3 ft, 4 ft and 9 ft.
Try These Determine if triangles can be formed with the following side lengths: 1. 4 cm, 7 cm, 10 cm 2. 24 mm, 20 mm, 30 mm Click 4 + 7 > 10 24 + 20 > 30 Click 4 + 10 > 7 24 + 30 > 20 7 + 10 > 4 20 + 30 > 24 YES YES 3. 7 ft, 9 ft, 16 ft 4. 9 in, 13 in, 24 in Click Click 7 + 9 = 16 9 + 13 < 24 7 + 16 > 9 9 + 24 > 13 16 + 9 > 7 13 + 24 > 9 NO NO
1 Determine if sides of length 5 mm, 14 mm and 19 mm can form a triangle. Be prepared to show your work! Yes No Answer
2 Determine if sides of length 6 in, 9 in and 14 in can form a triangle. Be prepared to show your work! Yes No Answer Yes
3 Determine if sides of length 5 yd, 13 yd and 21 yd can form a triangle. Be prepared to show your work! Yes No Answer No
4 Determine if sides of length 3 ft, 8 ft and 15 ft can form a triangle. Be prepared to show your work! Yes No Answer No
5 Determine if sides of length 5 in, 5 in and 9 in can form a triangle. Be prepared to show your work! Yes No Answer Yes
6 A triangle could have which of the following sets of angles? A 40º, 90º, 105º B 35º, 89º, 56º Answer C 75º, 90º, 15º B D 30º, 65º, 95º
7 A triangle could have which of the following sets of angles? A 37º, 63º, 80º B 90º, 104º, 76º C 23º, 47º, 50º Answer D 80º, 90º, 10º
Example Predict the length of the third side of a triangle with sides of length 12 ft and 16 ft. Side 1 = 12 ft Side 2 = 16 ft The 3rd side must be less than: 12 + 16 > 3rd side 28 ft > 3rd side The 3rd side must be greater than: 12 + 3rd side > 16 3rd side > 4 The 3rd side must be greater than 4 ft and less than 28 ft.
Example Predict the length of the third side of a triangle with sides of length 9 cm and 15 cm. Side 1 = 9 cm Side 2 = 15 cm The 3rd side must be less than: 9 + 15 > 3rd side 24 cm > 3rd side The 3rd side must be greater than: 9 + 3rd side > 15 3rd side > 6 The 3rd side must be greater than 6 cm and less than 24 cm.
Try These Predict the length of the third side of a triangle whose known sides are lengths: 1. 13 mm, 20 mm 2. 7 in, 19 in Click 13 + 20 > Side 3 7 + 19 > Side 3 Click 33 > Side 3 26 > Side 3 13 + Side 3 > 20 7 + Side 3 > 19 Side 3 > 7 Side 3 > 12 7 < side 3 < 33 12 < side 3 < 26
Try These Predict the length of the third side of a triangle whose known sides are lengths: 3. 4 ft, 11 ft 4. 23 cm, 34 cm Click Click 4 + 11 > Side 3 23 + 34 > Side 3 15 > Side 3 57 > Side 3 4 + Side 3 > 11 23 + Side 3 > 34 Side 3 > 7 Side 3 > 11 7 < side 3 < 15 11 < side 3 < 57
8 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m. Answer
9 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 6 m and 12 m. Answer 18 m
10 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in. Answer 8 in
11 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 9 in and 17 in. Answer
12 Predict the lower limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft. Answer 28 ft
13 Predict the upper limit of the length of the third side of a triangle whose known sides are lengths 15 ft and 43 ft. Answer 58 ft
Geometric Constructions: The Basics Return to Table of Contents
Geometric Tools In Geometry, we can draw just about every figure with various tools. The tools that we will be using are given on this slide & the Teacher Notes next slide: 1) Compass : creating circles & arcs 0° 86
Geometric Tools 2) Ruler : measure segments E DE = 6 cm D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0° 0 1 2 3 4 5 3) Protractor : measure angles 90 80 100 70 110 m ∠ ABC = 65° 60 120 90 100 80 110 7 0 50 130 120 60 A 4 0 140 130 50 140 40 0° 30 150 1 5 0 30 20 1 6 0 160 2 0 10 170 170 10 B 0 180 0 180 C
Example Draw a circle that has a radius of 6 cm. Step #1: Draw a segment with the ruler that measures 6 cm. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0° 0 1 2 3 4 5 Step #2: Line up your compass so that it's center tip lies on one endpoint & the pencil tip lies on the other endpoint. 0° 179
Step #3: Keeping the distance between the center & endpoint the same, draw your circle. 0° Teacher Notes 179
Radius Construct a circle that has a radius of 3 cm using a ruler & a compass. Circulate around the room to make sure that the students are constructing the circles Teacher Notes correctly. Figures should resemble the figure below.
Radius Construct a circle that has a radius of 8 cm using a ruler & a Circulate around the room to compass. make sure that the students are constructing the circles Teacher Notes correctly. Figures should resemble the figure below. Video: Constructing Circles
Example Use a ruler & a compass to draw an isosceles triangle with the following conditions: 1. at least one of the sides is 7 cm 2. at least one of the sides is 3 cm Step #1: Look at your conditions. Both of them say "at least one" which means that one side, or more sides could meet the conditions. Plus, since the triangle is isosceles, we know that two of the sides must be equal. So pick which number you want to occur for 2 of your sides. I'll select the 7 cm to occur twice. Step #2: Draw one of your 7 cm segments. A B 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0° 0 1 2 3 4 5
Step #3: With your compass, draw a circle or semicircle (whichever you prefer). 0° 211 A B Any segment that I connect from this arc to the center will have the same radius length of 7 cm.
15 1 4 1 3 5 1 2 Step #4: With your ruler, find the segment that can be drawn from B 11 4 to another point on the semicircle so that the ruler measures 3 cm. 1 0 Make a point at this location. 9 8 3 7 6 2 5 4 3 1 2 1 A B 9 9 ° 0 0 Step #5: Connect this point with points A & B to form your triangle. C A B Note: AC = AB = 7 cm , since they are both radii of the circle.
Think about this... Can we make a triangle if we use the 3 cm twice and the 7 cm once? Discuss this problem in your groups for a few minutes. Answer
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