Geometry
2.7: Prove Angle Pair Relationships
Investigate: Angles & Intersecting Lines
Name: _______________________________________________
Date: ________________________________________________
Essential Question: What is the relationship between the measures of the angles formed by intersecting
lines?
Sketch 1: Linear Pairs
1. Use the Line Tool to create a segment.
2. Use the Label Tool to label the endpoints A and B.
3. Draw a second segment, and label its endpoints C and D.
4. Use the Arrow Tool to highlight segments AB and CD.
From the Construct Menu choose intersection. Label the
intersection E.
5. Measure <AED. Use the Arrow Tool to highlight points
in THIS ORDER. A, E, D. From the Measure Menu, choose Angle. Measure the remaining 3
angles. Record the
measurements in the chart below.
Angle Measurement
Make Conclusions:
1. Describe the relationship between<AEC and <AED.
_________________________________________
2. Describe the relationship between <AED and <DEB.
_________________________________________
3. What do you notice about <AEC and <DEB?
_________________________________________
4. Move point C to a different position. Do the angle relationships stay the same?
______________
Make a conjecture: What is the relationship between 2 angles supplementary to the same angle?
Apply It! Use what you found to answer the question.
*If m<4 = 71, find m<1, m<2, and m<3.
Sketch 2: Complementary Angles
1. Use the Line Tool to draw a segment. Use the Label Tool to label
the endpoints A and B.
2. Use the Point Tool to create a point not on AB. Label the point C.
Use the Arrow to highlight segment AB and point C. From the
Construct Menu, choose Perpendicular Line.
3. Highlight the new line you just made. From the Construct Menu,
choose point on perpendicular line. Label the point D. Move D so
it is below segment AB. Use the Arrow Tool to highlight AB and CD.
From the Construct Menu, choose Intersection. Label the point E.
4. Use the Point Tool to draw a point not on either line. Label the point F.
5. Highlight points E and F. From the Construct Menu, choose Line. Use the
Point Tool to add another point to EF as shown. Label the point G.
6. Measure <AEF, <FED, <CEG, and <GEB. Record the angle measures in the chart below.
Angle
Measure
Draw Conclusions:
1. From the Measure Menu, choose calculate. Use the Arrow to highlight the measure of <AEG
and add it to the measure of <GEB. Repeat this step for the other two angles. What is the sum
of each pair?
Make a conjecture: What do you notice about angles formed by perpendicular lines?
2. Write your conjecture in an If-Then form.
3. What do you notice about <CEG and <DEF? What do you notice about <GEB and <FEA?
Apply It! Use what you discovered to solve the following problem.
**If m<3 = 30, then m<6 = ___________________
**If m<3 = 32, then m<2 = ___________________