Lines LaTeX: ACA C and LaTeX: DFD F are parallel. They are cut by transversal LaTeX: HJH J. 3 lines.Â
Find the seven unknown angle measures in the diagram. Explain your reasoning.

What do you notice about the angles with vertex LaTeX: BB and the angles with vertex LaTeX: EE?
Using what you noticed, find the measures of the four angles at point LaTeX: BB in the second diagram. Lines LaTeX: ACA C and LaTeX: DFD F are parallel.

3 lines in a plane.Â
The next diagram resembles the first one, but the lines form slightly different angles. Find the six unknown angles with vertices at points LaTeX: BB and LaTeX: EE.

Three lines in a plane.Â
What do you notice about the angles in this diagram as compared to the earlier diagram? How are the two diagrams different? How are they the same?

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)