Naming Angle Pairs in Parallel Lines.
(A). Consider triangle ABC below and follow the instructions.
(1). Without measuring, write what you think is the sum of the measures of these angles. Explain or show your reasoning.
(2). Is the measure of angle EAB equal to the measure of any angle in triangle ABC ? If so, which one? If not, how do you know?
(3). Is the measure of angle CAD equal to the measure of any angle in triangle ABC ? If so, which one? If not, how do you know?
(4). What is the sum of the measures of angles ABC, BAC, and ACB?
(B). Create a Few Quadrilaterals.
Use a protractor to measure the four angles inside the quadrilateral.
What is the sum of these four angle measures?
(A). Here is triangle △ABC. Line DE is parallel to line AC.
(1). What is m∠DBA + b + m∠CBE? Explain how you know.
(2). Use your answer to explain why a + b + c = 180.
(3). Explain why your argument will work for any triangle: that is, explain why the sum of the angle measures in any triangle is 180°.
(B). This diagram below shows a square BDFH that has been made by images of triangle ABC under rigid transformations.
Given that angle BAC measures 53 degrees, find as many other angle measures as you can.
For each triangle, find the measure of the missing angle.
Is there a triangle with two right angles? Explain your reasoning.
In the diagram below, lines AB and CD are parallel.
(1). What is mACE ?
(2). What is mACB ?
Here below is a diagram of triangle DEF.
(1). Find the measures of angles q, r, and s.
(2). Find the sum of the measures of angles q, r, and s.
(3). What do you notice about these three angles?