Download Geometry CC 1.8 Constructing parallel lines Opening Exercise

Geometry CC 1.8 Constructing parallel lines
Opening Exercise: Copy the angle below.
1.
2.
3.
4.
5.
Draw a ray.
Draw an arc that intersects both rays of the angle you wish to copy.
Using the same compass setting, draw an arc that intersects the ray draw in step 1.
Measure the distance between points of intersection (step 2) and transfer it to the angle you are constructing.
Draw a ray from the endpoint of the ray (step 1) through the point where the two arcs (step 3 and 4) intersect.
Recall: If two parallel lines are intersected by a transversal, the corresponding angles are congruent
Construct a line parallel to line t and passing through point P
̅̅̅̅ ≅ 𝐷𝐹
̅̅̅̅ ||𝐹𝐷
̅̅̅̅ , 𝐹𝑅
̅̅̅̅ ||𝐷𝐸
̅̅̅̅, and 𝐴𝐹
̅̅̅̅ . If 𝑚∠𝑅 = 105, find the measure of angle AFD .
1. a. In the diagram below, 𝑅𝐸
b. Explain how you found your answer. State the definitions, theorems and or postulates used to come up with
your solution.
2.
̅̅̅̅ and 𝐶𝐷
̅̅̅̅ intersect at E, and 𝐴𝐶
̅̅̅̅ ||𝐷𝐵
̅̅̅̅.
As shown in the diagram below, 𝐴𝐵
State all pairs of congruent angles.
̅̅̅̅ and 𝐶𝐷
̅̅̅̅ at G and H repectively. 𝐺𝐼
̅̅̅ is drawn such that Δ𝐻𝐺𝐼 is an
3. In the diagram below, ̅̅̅̅
𝐸𝐹 intersects 𝐴𝐵
isosceles triangle with vertex angle GHI.
If 𝑚∠𝐸𝐺𝐵 = 50o and 𝑚∠𝐷𝐼𝐺 = 115o , find 𝑚∠𝐺𝐻𝐼, 𝑚∠𝐻𝐺𝐼 and 𝑚∠𝐶𝐻𝐹.
4. Construct a line parallel to line t and passing through point P.