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Ms. Le’sFall 2017 CC Honors Geometry A: Unit 3 Parallel Lines Using GeoGebra
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I. Corresponding Angles: Quick Investigation
1. Use the Slope tool to measure the slopes of the two lines g and i. What do you notice?
2. What does your observation from (1) tell you about lines g and i?
3. If you haven't done so yet, drag the white point along transversal n as far as it will go. What geometric transformation is taking place?
4. If a transversal (in this case, n) intersects 2 lines that have the property that you wrote in response to (2) above, what can you conclude about the pair of orange corresponding angles that were formed?
II. Corresponding Angles Theorem (V2)
In the applet below, a TRANSVERSAL intersects 2 PARALLEL LINES. When this happens, there are 4 pairs of corresponding angles that are formed. Interact with the applet below for a few minutes, then answer the questions that immediately follow.
Directions & Questions:
1) Complete the following statement: If a transversal intersects 2 ______, then corresponding angles are ______.
2) If the pink angle above measures 52 degrees, what would the measure of its corresponding angle be? What would the measure of the gray angle be? 3) As you moved the slider, what transformation took place?
III. Alternate Interior Angles Theorem (V1) (V2) or (V3)
In the applet below, a TRANSVERSAL intersects 2 PARALLEL LINES. When this happens, there are 2 pairs of ALTERNATE INTERIOR ANGLES that are formed. Interact with the applet below for a few minutes, then answer the questions that immediately follow.
Directions & Questions:1) Complete the following statement: If a transversal intersects 2 ______, then alternate interior angles are ______. 2) If the pink angle above measures 134 degrees, what would the measure of its alternate interior angle be?
IV. Alternate Exterior Angles Theorem (V1) (V2) or (V3)
In the applet below, a TRANSVERSAL intersects 2 PARALLEL LINES. When this happens, there are 2 pairs of ALTERNATE EXTERIOR ANGLES that are formed. Interact with the applet below for a few minutes, then answer the questions that immediately follow.
Directions & Questions:
1) Complete the following statement: If a transversal intersects 2 ______, then alternate exterior angles are ______.
2) If the pink angle above measures 146 degrees, what would the measure of its alternate exterior angle be? What would the measure of the gray angle be? 3)As you moved the slider, what transformation(s) took place?
V. Same Side Interior Angles Theorem
In the applet below, a TRANSVERSAL intersects 2 PARALLEL LINES. When this happens, there are 2 pairs of SAME-SIDE INTERIOR ANGLES that are formed. Interact with the applet below for a few minutes, then answer the questions that immediately follow.
Directions & Questions:
1) Complete the following statement: If a transversal intersects 2 ______, then same-side interior angles are ______.
2) If the gray angle above measures 120 degrees, what would the measure of its same-side interior angle be?
3)As you moved the slider, what transformation(s) took place?
VI. Same Side Exterior Angles Theorem
In the applet below, a TRANSVERSAL intersects 2 PARALLEL LINES. When this happens, there are 2 pairs of SAME-SIDE EXTERIOR ANGLES that are formed. Interact with the applet below for a few minutes, then answer the questions that immediately follow.
Directions & Questions:
1) Complete the following statement: If a transversal intersects 2 ______, then same-side exterior angles are ______.
2) If the gray angle above measures 110 degrees, what would the measure of its same-side exterior angle be? 3) As you dragged the slider, what transformation(s) took place?