University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

419

Pages:

6
Author:

Arturo V

CONSTRUCTION #1: Segment Copy CONSTRUCTION Copy a Segment Step 1: Draw a segment XY. Elsewhere on your paper, draw a line and a point on the line. Label the point P. Step 2: Place the compass at point X and adjust the compass setting so that the pencil is at point Y. Step 3: Using that same compass setting, place the compass point at P and draw an arc that intersects the line. Label the point of intersection Q. Because of identical compass settings, PQ = XY. CONSTRUCTION Bisect a Segment Step 1: Draw a segment and name it XY. Place the compass at point X and adjust the compass setting so that its width is bigger than half but smaller than the segment. Draw arcs above and below XY. Step 2: Using the same compass setting, place the compass at point Y and draw arcs above and below XY that intersect the two arcs previously drawn. Label the points of intersection P and Q. Step 3: Use a straightedge to draw a line through points P and Q. This line intersects XY at M. Point M is the midpoint of XY, and PQ is the bisector of XY. Also, XM = MY = XY. CONSTRUCTION Copy an Angle Step 1: Draw an angle like ∠PQR on your paper. Step 2: Place the tip of the compass at point P and draw a large arc that intersects both sides of ∠PQR. Label the points of intersection Q and R. Step 3: Without changing the compass setting, place the compass point at T and draw a large arc that intersects ray TU. Label the point of intersection U. Step 4: Place the point of your compass on U and adjust so that the pencil tip is on R. Step 5: Without changing the compass setting, place the compass point at T and draw an arc that intersects the ray you drew in Step 3. Label the point of intersection V. Step 6: Use a straightedge to draw a ray from T through V. ∠UTV is congruent to ∠PQR. Practice: Construct copies of each of these angles: [Diagram of three angles: ∠E, ∠J, and ∠G] Video tutorials on 1.5 between example 2 and 3 CONSTRUCTION Bisect an Angle Step 1: Draw an angle and label the vertex as A. Put your compass point at point A and draw a large arc that intersects both sides of ∠A. Label the points of intersection B and C. Step 2: Keeping the same compass setting, place the compass point at point B and draw an arc in the interior of the angle. Step 3: Without changing the compass setting, place the compass point at point C and draw an arc that intersects the arc drawn in Step 2. Label the point of intersection D. Step 4: Draw AD. AD is the bisector of ∠A. Thus, m∠BAD = m∠DAC. Practice: Construct the bisectors of each of these angles: [Diagram of three angles: ∠T, ∠B, and ∠V] Video tutorials located on 1.5 between example 4 and 5