Unit 2: Angle Relationships and Parallel Lines
What a transversal does to two parallel lines, and how those angle patterns build toward every triangle and polygon angle sum.
7 topics · 25 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Parallel and Perpendicular Lines
- How it worksHow does comparing the slopes of two lines tell you if they're parallel or perpendicular?
- Worked exampleFind the slope of a line perpendicular to a line with slope 2/3.
- Common mistakeWhy doesn't a small angle drawn between two lines on paper mean they're close to parallel?
- Going furtherWhat happens to two parallel lines when they're both reflected across a third line?
Your turn1 of 2
Find the slope of a line perpendicular to a line with slope 7/6.Classifying Triangles by Sides and Angles
- How it worksHow do scalene, isosceles, and equilateral sort triangles by side length while acute, right, and obtuse sort them by angle?
- Worked exampleShow how a triangle with sides 5, 5, and 8 and angles 46, 46, and 88 degrees is classified by both its sides and its angles.
- Common mistakeWhy can't a triangle ever be classified as both right and equilateral at the same time?
Your turn1 of 2
A triangle has two sides that each measure 11 units, and a third side of a different length. By its SIDES, how should this triangle be classified?Angles Formed by a Transversal
- How it worksHow do corresponding angles line up in matching corners when a transversal crosses parallel lines?
- How it worksHow do alternate interior angles end up congruent even though they sit on opposite sides of the transversal?
- Worked exampleFind all eight angle measures when a transversal crosses two parallel lines and one angle measures 62 degrees.
- Common mistakeWhy aren't same-side interior angles congruent the way alternate interior angles are?
Your turn1 of 2
A transversal crosses two parallel lines. One angle measures 121 degrees. Find the measure of its same-side (consecutive) interior angle.Proving Two Lines Are Parallel
- How it worksHow does the converse of the corresponding angles theorem let you prove lines parallel from angle measures alone?
- Worked exampleFind the value of x that makes two lines parallel if alternate interior angles measure 3x + 10 and 5x - 20.
- Common mistakeWhy doesn't a pair of supplementary angles at a crossing automatically prove the lines are parallel?
Your turn1 of 2
Two lines are cut by a transversal. A pair of alternate interior angles measure 3x + 12 degrees and 5x - 12 degrees. Find the value of x that makes the two lines parallel.The Parallel Postulate
- How it worksHow does the parallel postulate guarantee exactly one line through a point that never meets a given line?
- Going furtherWhat happens to the parallel postulate on the curved surface of a sphere?
- Ties togetherHow does dropping the parallel postulate change the angle sum of a triangle drawn on a globe?
Your turn1 of 2
According to the Parallel Postulate, how many lines through a point NOT on line L will never intersect line L?Triangle Angle Sum and the Exterior Angle Theorem
- How it worksHow does drawing a line through one vertex parallel to the opposite side prove the triangle angle sum?
- Worked exampleFind the missing angle in a triangle with angles of 48 degrees and 67 degrees.
- Worked exampleFind the exterior angle of a triangle whose two remote interior angles measure 55 and 40 degrees.
- Common mistakeWhy isn't an exterior angle of a triangle just 180 degrees minus a random interior angle?
Your turn1 of 2
A triangle has two angles measuring 69 degrees and 59 degrees. Find the measure of the third angle.Interior and Exterior Angle Sums of Polygons
- How it worksHow does splitting a polygon into triangles from one vertex give a formula for its interior angle sum?
- Worked exampleFind the sum of the interior angles of a regular octagon.
- Worked exampleFind the measure of one interior angle of a regular decagon.
- Common mistakeWhy doesn't the sum of a polygon's exterior angles change as you add more sides?
Your turn1 of 2
Find the sum of the interior angles of a regular polygon with 15 sides.