1 / 14

Triangle Sum Theorem & Exterior Angle Theorem

Triangle Sum Theorem & Exterior Angle Theorem. 3. 1. 2. 4. 5. 90°. 40°. 40°. 50 °. 130°. 90°. 50 °. Work in groups to answer the questions. Try your best. Name 2 pair of alternate interior angles  5 &  3 and  4 &  1 2. What is the sum of m  1 + m  2 + m  3?

lmoller
Download Presentation

Triangle Sum Theorem & Exterior Angle Theorem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Triangle Sum Theorem&Exterior Angle Theorem

  2. 3 1 2 4 5 90° 40° 40° 50° 130° 90° 50° Work in groups to answer the questions. Try your best. • Name 2 pair of alternate interior angles 5 & 3 and 4 & 1 2. What is the sum of m1 + m2 + m3? 180° • If m4 = 65° and m5 = 50°, what is m2? 65° 50° 4. Find all the angle measures 40°

  3. Vocabulary • Adjacent angles – angles that share a common vertex and side • Verticalangles – a pair of non-overlapping angles that are opposite and congruent to each other when two lines intersect • Complementaryangles – two angles whose sum of angle measures equals 90 degrees • Supplementaryangles – two angles whose sum of angle measures equals 180 degrees • Congruentangles – angles whose angle measurements are equal

  4. continued . . . • Axes – the vertical and horizontal lines that act as a reference when plotting points on a coordinate plane • Exterior angles of a triangle – angles that are outside of a triangle between one side of a triangle and the extension of the adjacent side • Interior angles of a triangle – angles that are inside of a triangle, formed by two sides of the triangle • Transversal – a line that intersects two or more lines • Angle-angle criterion for triangles – if two angles in one triangle are congruent to two angles in another triangle, then the measure of the third angle in both triangles are congruent

  5. Objectives---What we’ll learn… • Find the measurement of a missing angle by using Triangle Angle Sum Theorem. • Find the measurement of a missing angle by using Exterior Angle Theorem.

  6. 1 3 2 Triangle Sum Theorem The sum of the angle measures in a triangle equal 180° 1 + 2 + 3 = 180°

  7. Isosceles Triangles 2 congruent sides 2 congruent base angles

  8. Isosceles Triangles & Angle Sum Theorem Base Angles are congruent. W  H E + W + H = 180o E + 2(W) = 180o

  9. exterior angle remote interior angles Exterior Angle Theorem The measure of an exterior angle in a triangle is the sum of the measures of the 2 remoteinterior angles A = C + D

  10. exterior angle remote interior angles 2 1 3 4 Exterior Angle Theorem The measure of an exterior angle in a triangle is the sum of the measures of the 2 remoteinterior angles 4 = 1 + 2

  11. Example 1 on Exterior Angle

  12. Example 2 on Exterior Angle

  13. Shortcut: 1. Triangle INTERIOR Angle Sum 2. Triangle EXTERIOR Angle Sum

  14. X 60º 42º y an example with numbers find x & y 82° x = 68° y = 112° 30° x y

More Related