N-Gen-Math-8.Unit-2.Lesson-4.Geometric-Terminology.pdf
Microsoft Word - Math 8.Unit 2.Lesson 4.Geometric Terminology Name: ______________________________ Date: _____________________ N-GEN MATH™ 8, UNIT 2 – TOOLS OF GEOMETRY - LESSON 4 eMATHINSTRUCTION™, RED HOOK, NY 12571, © 2020 ® ® GEOMETRIC TERMINOLOGY N-GEN MATH 8 In all areas of math, terminology is important to know and understand. Terminology is just a fancy word for the specific vocabulary that applies to a certain set of knowledge or study. You’ve already seen a lot of geometric terminology, such as line, ray, point, segment, and angle. In this lesson we will learn additional terms that we need to know to study geometry. Exercise #1: The diagram below shows segment AB with point M plotted on it. A 10 cm ruler is given for measurement purposes. (a) What is the length of AB ? This is known as the measure of the segment. AB Every line segment has one unique point that lies at its center or middle known as its midpoint. Exercise #2: In the diagram below points A, B, C, D, and E all lie on a straight line (are all collinear). Point C is the midpoint of AB , point D is the midpoint of AC and point E is the midpoint of CD . If the length of AB is 40 then what is the length of EB? Exercise #3: Why do segments have midpoints, but lines do not? (b) What is the measure of segments AM and BM ? AM BM (c) Point M is called the midpoint of segment AB . Why does this term make sense? N-GEN MATH™ 8, UNIT 2 – TOOLS OF GEOMETRY - LESSON 4 eMATHINSTRUCTION™, RED HOOK, NY 12571, © 2020 ® ® ® ® Another important idea in geometry is that of a bisector. As its name implies, a bisector cuts a geometric object into two of the same types of objects that have the same measure. We can have segment bisectors (other segments or lines) and angle bisectors (lines, segments, or rays). Exercise #4: In the diagram below BAC has ray AD drawn from its vertex point A. (a) What is the measure of BAC ? (b) Explain how you can tell that AD bisects BAC . Exercise #5: In the diagram below segment CD bisects segment AB . Based on this information, which of the following pairs of segments must have the same length? Explain your choice. (1) AB and CD (2) CE and DE (3) AE and BE (4) DE and BE Our final piece of terminology is the term perpendicular. This describes two lines, segments, or rays that form right angles with one another. Exercise #6: In the diagram below A, B, and C lie on a straight line. The measure of EBC is 58 and the measure of ABD is 30 . Are rays BD and BE perpendicular? Justify your answer. Name: ______________________________ Date: _____________________ N-GEN MATH™ 8, UNIT 2 – TOOLS OF GEOMETRY - LESSON 4 eMATHINSTRUCTION™, RED HOOK, NY 12571, © 2020 ® ® GEOMETRIC TERMINOLOGY N-GEN MATH 8 HOMEWORK FLUENCY 1. In the diagram below point C is the midpoint of AB . If the length of AB is 32 and the length of AC is given by 10 2 x then which of the following is the value of x? (1) 11 (3) 3 (2) 12 (4) 44 2. Points M, R, P, Q, and N all lie on a straight line. Point P is the midpoint of segment MN . As well, point Q is the midpoint of segment PN . Finally, point R is the midpoint of segment MQ . If the length of MN is 24 units, which of the following is the length of MR ? (1) 6 (3) 10 (2) 9 (4) 12 3. In the diagram below, ray AB bisects MAT . If the measure of MAT equals 64 and the measure of BAT is given by the expression 2 10x , then which of the following is the value of x? (1) 14 (2) 15 (3) 21 (4) 37 4. In the diagram shown, ray CD is perpendicular to ray CE . If the measure of DCF is 115 then what is the measure of ECF ? N-GEN MATH™ 8, UNIT 2 – TOOLS OF GEOMETRY - LESSON 4 eMATHINSTRUCTION™, RED HOOK, NY 12571, © 2020 ® ® ® ® 5. In the diagram shown, rays AD and AC are perpendicular. Ray AE bisects DAC and the measure of DAB is 30 . What is the measure of BAE ? Justify. USING YOUR MATH 6. The diagonals of a parallelogram bisect each other. In the diagram below, parallelogram ABCD has diagonals AC and BD whose lengths are 12 inches and 24 inches, respectively. What is the perimeter of triangle BEC? REASONING 7. Given all the rays starting at point M below, which pair are perpendicular? Justify how you can tell from the angle measurements.