Practice: Angle Relationships in Triangles
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1 Name: 1 Date: Practice: Angle Relationships in Triangles BLM (page 1) 1. Find the measure of each indicated exterior angle. c) d) e) f) 2. Find the measure of each indicated exterior angle. c) d) e) f) Principles of Mathematics 9: Teacher s Resource BLM Practice: Angle Relationships in Triangles Copyright 2006 McGraw-Hill Ryerson Limited.
2 Name: Date: 2 3. Find the measure of each indicated exterior angle. BLM (page 2) c) d) 4. Find the measure of each indicated angle. c) d) 5. One interior angle in an isosceles triangle measures 42. Find the possible measures for the exterior angles. Principles of Mathematics 9: Teacher s Resource BLM Practice: Angle Relationships in Triangles Copyright 2006 McGraw-Hill Ryerson Limited.
3 Name: 3 Date: Practice: Angle Relationships in Quadrilaterals BLM (page 1) 1. Find the measure of each indicated angle. c) d) 2. Find the measure of each indicated exterior angle. c) d) Principles of Mathematics 9: Teacher s Resource BLM Practice: Angle Relationships in Quadrilaterals Copyright 2006 McGraw-Hill Ryerson Limited.
4 Name: Date: 4 BLM (page 2) 3. The measures of three interior angles of some quadrilaterals are given. Find the measure of the fourth interior angle for each quadrilateral. a) 110, 80, 75 b) 95, 95, 150 c) 68, 29, 103 d) 132, 48, The measures of the exterior angles at three vertices of some quadrilaterals are given. Find the measure of the exterior angle at the fourth vertex. a) 75, 125, 35 b) 50, 145, 85 c) 76, 34, 178 d) 93, 83, Find the measure of each indicated angle. c) d) 6. Find the measure of each indicated angle. c) d) Principles of Mathematics 9: Teacher s Resource BLM Practice: Angle Relationships in Quadrilaterals Copyright 2006 McGraw-Hill Ryerson Limited.
5 Name: 5 Date: Practice: Angle Relationships in Polygons BLM Find the sum of the interior angles of each polygon. c) d) 2. Find the sum of the interior angles of each polygon. c) d) 3. Find the sum of the interior angles of a polygon with each number of sides. a) 11 sides b) 14 sides c) 18 sides d) 24 sides 4. Find the measure of each interior angle of a regular polygon with each number of sides. a) 3 sides b) 20 sides c) 9 sides d) 16 sides 5. Find the number of sides each polygon has given the sum of its interior angles. a) 720 b) 1980 c) 2340 d) 4140 Principles of Mathematics 9: Teacher s Resource BLM Practice: Angle Relationships in Polygons Copyright 2006 McGraw-Hill Ryerson Limited.
6 Classifying Triangles 6 Classify each triangle by side length AND by angle
7 Midpoints, Medians, and Diagonals in Polygons Adjacent Median Perpendicular Triangle Bisect Midpoint Polygon Vertex Diagonal Parallelogram Quadrilateral Term Definition Examples Non-Examples Any enclosed 2D shape made up of straight lines 1 7 A corner of a 2D or 3D shape Any enclosed figure with three straight sides. The sum of the interior angles is 180 Any enclosed figure with four straight edges. The sum of the interior angles is 360 Any 4-sided figure with two pairs of parallel sides Next to; beside A line joining two vertices of a polygon that are not next to each other The points on a line segment that is in the middle of the two endpoints A line segment joining a vertex of a triangle to the opposite side s midpoint Two lines that meet at a 90 angle To divide in half
8 Midpoints and Medians in Triangles 2 8 Connecting adjacent midpoints: A Connect the midpoints of AB and AC. Label it DE. C What do you notice about BC and DE? B What do you notice about the distance from points A to DE, and the distance between DE and BC? RULE: Drawing medians: Draw a median from Point F. Label the new point I. F Now ΔFGI and ΔFHI have... G RULE: H
9 Midpoints and Medians in Triangles In areas that get a lot of snow, cottages are often built with a triangular shape called an A-frame. This shape helps prevent damage from heavy loads of snow on the roof. a) Find the width of the floor of the upper room in this cottage. b) Find the height of the upper room. 2. The area of ΔABC is 45cm a) Calculate the area of ΔABS. b) Calculate the area of ΔACS
10 Name: 10 Date: Practice: Midpoints and Medians in Triangles BLM Find the length of line segment MN in each triangle. c) d) 2. Find the lengths of line segments AD and DE in each triangle. c) d) 3. The area of ABC is 10 cm 2. Calculate the area of each triangle. a) ABD b) ADC 4. Calculate the area of each triangle given the area of MNQ is 12 cm 2. a) MNP b) NPQ 5. Here are two conjectures about a median in an isosceles triangle. For each conjecture, explain why the conjecture is true, or draw a counterexample to show it is false. a) The median to the vertex opposite the unequal side bisects the angle. b) The median to a vertex opposite one of the equal sides bisects the angle. Principles of Mathematics 9: Teacher s Resource BLM Practice: Midpoints and Medians in Triangles Copyright 2006 McGraw-Hill Ryerson Limited.
11 Midpoints and Diagonals in Quadrilaterals 4 11 Connecting adjacent midpoints: Draw line segments to connect the adjacent midpoints in this quadrilateral. What do you notice about the new shape you made? RULE: Drawing diagonals: Draw diagonals for this parallelogram. Label the point where they intersect as N. J K What do you notice about the length of JN and NM? L M RULE:
12 Midpoints and Diagonals in Quadrilaterals Which line segments are parallel in the following diagram? 2. Calculate the lengths of EC and ED given that AC measures 88cm and BD measures 80cm.
13 Name: 13 Date: Practice: Midpoints and Diagonals in Quadrilaterals BLM Which line segments in each diagram are parallel? a) 3. Calculate the length of each line segment given that RU = 3.6 cm and RT = 6 cm. b) 2. Find the measures of the indicated angles. a) a) SR b) SU c) VR d) VT 4. Calculate the length of each line segment given that AC = 13.2 m and XD = 6.6 m. b) a) AX b) XC c) BX d) BD 5. Explain why each statement is true or draw a counterexample to show it is false. a) The diagonals of a rectangle are perpendicular to one another. b) The diagonals of a square are perpendicular to one another. Principles of Mathematics 9: Teacher s Resource BLM Practice: Midpoints and Diagonals in Quadrilaterals Copyright 2006 McGraw-Hill Ryerson Limited.
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You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
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