1 / 12

Understanding and Classifying Triangles: Types and Properties

This guide covers the essential concepts of classifying triangles based on their sides and angles. A triangle is defined as a polygon with three sides, and its corners are known as vertices. Learn to classify triangles into categories like scalene, isosceles, right, acute, and obtuse through given examples and practical exercises. Additionally, explore how to apply the distance formula to find side lengths in a coordinate plane and how to determine whether a triangle is a right triangle based on the slopes of its sides.

jesse-hendrix
Download Presentation

Understanding and Classifying Triangles: Types and Properties

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. 4.1 – Classifying Triangles

  2. Triangles • A polygon with three sides. • The corners are called vertices • A triangle with vertices A, B, and C is called “triangle ABC” or “

  3. Classifying Triangles by Sides

  4. Classifying Triangles by Angles

  5. Example 1:Classify triangles by sides and angles a) b) c) 7 40° 15° 25 24 70° 70° 120° 45° • Solutions: • Scalene, Right • Isosceles, Acute • Scalene, Obtuse

  6. Example 2:Classify triangles by sides and angles Now you try… a) b) c) 5 110° 3 5 5 4 5

  7. Review: The distance formula To find the distance between two points in the coordinate plane…

  8. Classify PQOby its sides. Then determine if the triangle is a right triangle. Use the distance formula to find the side lengths. STEP1 2 2 – – ( ( ) ) OP = + + 2 2 – – ( ( ) ) y x x y y y x x 2 1 2 2 2 1 1 1 2 2 ( – ( ) (– 1 ) ) 0 2 – 0 2.2 + = = 5 OQ = 2 2 ( – ( ) 6 ) 0 – 0 3 6.7 + = = 45 EXAMPLE 3 Classify a triangle in a coordinate plane SOLUTION

  9. PQ = 2 2 ( – ) 6 (– 1 ) ) 3 – ( 2 7.1 + = = Check for right angles by checking the slopes. There is a right angle in the triangle if any of the slopes are perpendicular. STEP2 The slope ofOPis 2 – 0 3 – 0 1 . – 2. The slope ofOQis = = – 2 – 0 2 6 – 0 2 – ( ) + 2 – ( ) so OPOQand POQ is a right angle. y y x x 1 1 2 2 50 ANSWER Therefore, PQOis a right scalene triangle. EXAMPLE 3 Classify a triangle in a coordinate plane (continued)

  10. Example 4:Classify a triangle in the coordinate plane Now you try… Classify ΔABC by its sides. Then determine if the triangle is a right triangle. The vertices are A(0,0), B(3,3) and C(-3,3). Step 1: Plot the points in the coordinate plane.

  11. Example 4: (continued)Classify a triangle in the coordinate plane Step 2: Use the distance formula to find the side lengths: AB = BC = CA = Therefore, ΔABC is a ______________ triangle.

  12. Example 4: (continued)Classify a triangle in the coordinate plane Step 3: Check for right angles by checking the slopes. The slope of = The slope of = The slope of = Therefore, ΔABC is a ______________ triangle.

More Related