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Constructions 6 Name:____________________________ Date:______________ OBJECTIVE: SWBAT copy an angle using constructions. OPENING EXERCISE In the following figure, circles have been constructed so that the endpoints of the diameter of each circle coincide with the endpoints of each segment of the equilateral triangle. A. What is special about points ๐ซ, ๐ฌ, and ๐ญ? Explain how this can be confirmed with the use of a compass. B. Using a straightedge, draw DE, EF, and FD. What kind of triangle must โณ DEF be? C. What is special about the four triangles within โณ ABC? D. How many times greater is the area of โณ ABC than the area of โณ CDE? Page 1 of 7 Constructions 6 HOW TO COPY AN ANGLE [You will need a compass and a straightedge] FOLLOW THE GIVEN STEPS TO COPY THE ANGLE: 1. Label the vertex of the original angle as ๐ฉ. โโโโโ as one side of the angle to be drawn. 2. Draw ๐ฌ๐ฎ 3. Draw an arc from vertex ๐ฉ, any size through the angle. 4. Label the intersections of the arc with the sides of the angle as ๐จ and ๐ช. 5. Draw an arc of same size from point E. โโโโโ as ๐ญ. 6. Label intersection of the arc with ๐ฌ๐ฎ ฬ. 7. Draw an arc from point F, the same span size as ๐ช๐จ 8. Label intersection of arcs as ๐ซ. 9. Draw โโโโโโ ๐ฌ๐ซ. Page 2 of 7 Constructions 6 Copy the given angle and measure both angles to confirm. Given Copy 1. What is the measure of the angle?____ 2. Page 3 of 7 What is the measure of the angle?____ Constructions 6 COPY THE GIVEN FIGURE IN THE BOX INTO THE NEXT BOX. 3. COPY 4. COPY 5. COPY Page 4 of 7 Constructions 6 6. Using your knowledge of copying an angle, construct a line parallel to the line through point A. 1. Draw a diagonal line through A 2. Draw an arc from the lower angle 3. Copy the arc from A intersecting the diagonal line at “B” 4. Measure the 1st arc 5. Put center at “B” and copy the arc intersecting at “C” 6. Connect A to the intersection at “C” A โ1 7. Construct a line parallel to the line through point A. A โ1 Page 5 of 7 Constructions 6 Problem Set 1. Which construction of parallel lines is justified by the theorem “If two lines are cut by a transversal to form congruent alternate interior angles, then the lines are parallel. 1. 2. 3. 4. 2.The diagram shows the construction of a line m, parallel to line l, through point P. Which theorem was used to justify this construction? 1. If two lines are cut by a transversal and the alternate interior angles are congruent, then lines are parallel. 2. If two lines are cut by a transversal and the interior angles on the same side are supplementary, the lines are parallel. 3. If two lines are cut by a transversal and the corresponding angles are congruent, they are parallel. 4. If two lines are perpendicular to the same line they are parallel. โกโโโโ through point P. 3. The diagram illustrates the construction of โกโโโ ๐๐ parallel to ๐ ๐ Which statement justifies this construction? 1) m<1 = m<2 Page 6 of 7 2) m<1 =m<3 ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ≅ ๐ ๐ 3) ๐๐ ฬ ฬ ฬ ฬ ≅ ๐ ๐ ฬ ฬ ฬ ฬ 4) ๐๐ Constructions 6 4. The diagram shows the construction of โกโโโโ ๐ด๐ต through point P parallel to โกโโโโ ๐ถ๐ท. Which theorem justifies this method of construction? 1. If two lines in a place are perpendicular to a transversal at different points, then the lines are parallel. 2. If two lines in a plane are cut by a transversal to form congruent corresponding angles, then the lines are parallel. 3. If two lines in a place are cut by a transversal to form congruent alternate interior angles, then the lines are parallel. 4. If two lines in a place are cut by a transversal to form congruent alternate exterior angles, then the lines are parallel. 5. Using a compass and straightedge, construct a line parallel to the line through point A. A โ1 Page 7 of 7