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Do Now • Write homework in your agenda • Take out Triangle Angles HW from yesterday • Prepare to ask questions
Parallel Lines & Transversals Intro • https: //www. youtube. com/watch? v=5 Pc. Mb. N 46 NMA
Vocabulary Review
A right angle measures 90°. Reading Math A right angle can be labeled with a small box at the vertex.
Acute Angles – measure less than 90 degrees. Obtuse Angles – measure more than 90 degrees.
1 st & 2 nd Tabs in Vocab Flip Book
Complementary angles: Angles whose measures sum to 90°. A right angle measures 90°. Angle symbol ∡ Supplementary angles: Angles whose measures sum to 180°. A straight line measures 180°.
3 rd Tab in Vocab Flip Book
Vertical Angles: Angles formed by 2 intersecting lines. Vertical angles are always congruent. Congruent Symbol: ≅ In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.
Example: Finding the Measure of Vertical Angles In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles. If m 1 = 37°, find m 3. 1 and 3 are vertical angles. m 3 = 37°
4 th Tab in Vocab Flip Book
Parallel lines are lines in a plane that never meet, like a set of perfectly straight, infinite train tracks. The symbol for parallel is ||.
The railroad ties are transversals to the tracks. The tracks are parallel. A transversal is a line that intersects 2 or more lines in the same plane. It creates angles with special properties when it intersects parallel lines.
Example: Identifying Congruent Angles Formed by a Transversal Look at the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 1, 3, 5, and 7 all measure 150°. 2, 4, 6, and 8 all measure 30°.
Example Continued Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other. 1 @ 3 @ 5 @ 7 2 @ 4 @ 6 @ 8 2 1 3 4 6 5 7 8
5 th Tab in Vocab Flip Book
Perpendicular lines: Lines that intersect at 90° angles. The symbol for perpendicular is . Coincidental Lines are the same line.
6 th Tab in Vocab Flip Book
Alternate interior angles: 2 angles on opposite sides of the transversal and inside the parallel lines. These angles are ≌. The pair of blue and the pair of pink angles are alternate interior angles.
7 th Tab in Vocab Flip Book
Alternate exterior angles: 2 angles on opposite sides of the transversal and outside the parallel lines. These angles are ≌. The pair of blue and the pair of pink angles are alternate exterior angles.
8 th Tab in Vocab Flip Book
Corresponding angles: Angles in matching corners when 2 parallel lines are crossed by a transversal. Corresponding angles are ≌. The pair of pink angles are corresponding. The pair of purple angles are corresponding. The blue pairs and green pairs are also corresponding.
Other Angles
Same side interior or consecutive interior angles are 2 angles inside the 2 parallel lines along the same side of a transversal line. These angles are supplementary. 1 2 3 4 5 6 7 8 Ex: <3 and <5 are same side interior angles. <4 and <6 are same side interior angles.
Same side exterior or consecutive exterior angles are 2 angles outside the 2 parallel lines along the same side of a transversal line. These angles are supplementary. 1 2 3 4 5 6 7 8 Ex: <1 and <7 are same side exterior angles. <2 and <8 are same side exterior angles.
Example: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l (L) || line m. Find the measure of the angle 4. All obtuse angles in the figure are congruent. m 4 = 124°
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