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Understanding Polygons and Triangles: Definitions and Classifications in Geometry

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kai-hunt
16 diapositives · 289 Views · Nov 18, 2014

In this lesson presentation, we explore foundational concepts in geometry, including the properties of six-sided polygons and the classification of angles and triangles. Students will learn about hexagons and the definitions of acute angles, supplementary angles, and various types of triangles: scalene, isosceles, and equilateral, based on their sides and angles. Through examples and interactive classifications, learners will deepen their understanding of geometric shapes and their properties, aligning with California standards for geometrical reasoning.

#understanding polygons and triangles: definitions and classifications in geometry #understanding polygons and triangles: definitions and classifications in geometry ppt #powerpoint #presentation
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Understanding Polygons and Triangles: Definitions and Classifications in Geometry
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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up 1.What is the name of a six-sided polygon? 2. What is the definition of an acute angle? 3. The measure of one of two supplementary angles is 32°. What is the measure of the other angle? hexagon an angle that measures less than 90° 148°

  3. California Standards Preparation for MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle.)

  4. Vocabulary scalene triangle isosceles triangle equilateral triangle acute triangle obtuse triangle right triangle

  5. One way to classify triangles is by the lengths of their sides. Triangles classified by sides A scalene triangle has no congruent sides.

  6. One way to classify triangles is by the lengths of their sides. Triangles classified by sides An isosceles triangle has at least 2 congruent sides.

  7. One way to classify triangles is by the lengths of their sides. Triangles classified by sides In an equilateral triangle, all of the sides are congruent.

  8. One way to classify triangles is by the lengths of their sides. Another way is by the measures of their angles. Triangles classified by angles In an acute triangle, all of the angles are acute.

  9. One way to classify triangles is by the lengths of their sides. Another way is by the measures of their angles. Triangles classified by angles An obtuse trianglehas one obtuse angle.

  10. One way to classify triangles is by the lengths of their sides. Another way is by the measures of their angles. Triangles classified by angles A right triangle has exactly one right angle.

  11. Additional Example 1: Classifying Triangles Classify each triangle according to its sides and angles. Two congruent sides A. isosceles acute Three acute angles This is an isosceles acute triangle. B. scalene No congruent sides right One right angle This is a scalene right triangle.

  12. Additional Example 1: Classifying Triangles Classify each triangle according to its sides and angles. equilateral Three congruent sides C. acute Three acute angles This is an equilateral acute triangle. D. scalene No congruent sides right One right angle This is a scalene right triangle.

  13. Check It Out! Example 1 Classify each triangle according to its sides and angles. isosceles Two congruent sides A. obtuse One obtuse angle This is an isosceles obtuse triangle. Two congruent sides B. isosceles right One right angle This is an isosceles right triangle.

  14. Check It Out! Example 1 Classify each triangle according to its sides and angles. scalene No congruent sides C. obtuse One angle exceeding 90° This is a scalene obtuse triangle. scalene D. No congruent sides obtuse One angle exceeding 90° This is a scalene obtuse triangle.

  15. Additional Example 2: Identifying Triangles Identify the different types of triangles in the figure, and determine how many of each there are. 2 Scalene ABD, CBD Isosceles 2 ACE, ABC Right 2 ABD, CBD Obtuse 1 ACE Acute 1 ABC

  16. DJA, JDG HJI, BCD DFE DJA, ADG JDG, JHI, BCD, DEF Check It Out! Example 2 Identify the different types of triangles in the figure, and determine how many of each there are. A Type How many Name B I J C Isosceles 5 D H F 2 G Obtuse E Acute 4