Triangles
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Triangles have three sides and are polygons. Two triangles are congruent if they have the same shape and size. Similar triangles have the same shape but not necessarily the same size, with equal corresponding angles and proportional corresponding sides. The document discusses similar triangles and figures, basic theorems, examples, and proves the basic proportionality theorem.
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1) A triangle is a three-sided polygon with three vertices and three edges.
2) Triangles can be classified based on side lengths (equilateral, isosceles, scalene) or interior angles (right, acute, obtuse).
3) The interior angles of any triangle always sum to 180 degrees. Congruent triangles have the same shape and size, while similar triangles have the same angle measures but sides proportional in length.
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This document defines and describes different types of triangles based on their side lengths and angles. It explains that a triangle can be equilateral, isosceles, or scalene depending on whether its sides are all equal, two sides are equal, or all sides are unequal. It also defines right, obtuse, and acute triangles based on whether they have one 90 degree angle, one angle over 90 degrees, or all angles under 90 degrees.
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The document discusses different criteria for determining similarity and congruence of triangles:
1) AA and SSS criteria state that triangles are similar if corresponding angles or sides are proportional.
2) SAS criterion states triangles are congruent if two sides and the included angle are equal.
3) SSS, ASA, and HL criteria also determine triangle congruence if three sides, two angles and included side, or hypotenuse and leg are equal.
The document also discusses scale factors in similar figures and angle relationships formed by parallel lines cut by a transversal.
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- Exterior angles on the same side of the transversal are supplementary
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1) A triangle is a three-sided polygon with three vertices and three edges.
2) Triangles can be classified based on side lengths (equilateral, isosceles, scalene) or interior angles (right, acute, obtuse).
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This document defines and describes different types of triangles based on their side lengths and angles. It explains that a triangle can be equilateral, isosceles, or scalene depending on whether its sides are all equal, two sides are equal, or all sides are unequal. It also defines right, obtuse, and acute triangles based on whether they have one 90 degree angle, one angle over 90 degrees, or all angles under 90 degrees.
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The document discusses different criteria for determining similarity and congruence of triangles:
1) AA and SSS criteria state that triangles are similar if corresponding angles or sides are proportional.
2) SAS criterion states triangles are congruent if two sides and the included angle are equal.
3) SSS, ASA, and HL criteria also determine triangle congruence if three sides, two angles and included side, or hypotenuse and leg are equal.
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The document contains information about using similarity postulates to determine if triangles are similar and find unknown side lengths. It provides examples of using the AA, SAS, and SSS similarity postulates to show triangles are similar. It also shows using proportional sides to find missing lengths. The objective is for students to use similarity postulates to decide if triangles are similar and find unknowns.
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This document discusses three rules for determining if triangles are similar: the AA Similarity Postulate, SAS Similarity Theorem, and SSS Similarity Theorem. It provides examples of applying each rule to determine if triangles are similar, and if so, writing the similarity statement and ratio.
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If parallel lines are cut by a transversal, then:
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Triangles
- 1. TRIANGLES
- 2. Triangles A triangle is a three sided closed polygon . Two triangles are said to be congruent, if they have the same shape and the same size. Two triangles having the same shape (but not necessarily the same size) are called similar triangles.
- 4. Similar triangles Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional.
- 9. NOW…
- 10. Hence Proved…….
- 11. Now….
- 12. [Basic proportionality Theorem] [Basic proportionality Theorem] Hence Proved…….