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Geometry Extra Credit Chapter 3

Geometry Extra Credit Chapter 3. Lexy Smith Jacob Langer Mr.Bianco Pd. 7 December 16, 2012. Triangle Theorems and Postulates. Triangle Inequality Postulate - The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

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Geometry Extra Credit Chapter 3

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  1. Geometry Extra CreditChapter 3 Lexy Smith Jacob Langer Mr.Bianco Pd. 7 December 16, 2012

  2. Triangle Theorems and Postulates • Triangle Inequality Postulate - The sum of the lengths of any two sides of a triangle is greater than the length of the third side. • SSS (Side SideSide)Postulate – If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent. • SAS (Side Angle Side) Postulate – If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle then the triangles are congruent. • ASA (Angle Side Angle)Postulate – If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent. • Figures are congruent if all corresponding sides are congruent. • AAS (Angle Angle Side) Theorem – If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle then the triangles are congruent.

  3. Triangle Theorems and Postulates • CPCTC – Corresponding parts of congruent triangles are congruent. • Vertex Angles – Angles that are always included between congruent sides. • Isosceles Triangle Theorem – If two sides of a triangle are congruent, then the angles opposite those sides are congruent. • Converse of The Isosceles Triangle Theorem – If two angles are congruent, then the sides opposite those two sides are congruent. • The angle bisector of the vertex angle is the angle bisector of the base. • Vertex Angle– Angle that is always included between to congruent sides. • HL (Hypotenuse Leg) Theorem – If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

  4. Triangle Vocabulary and Theorems Auxiliary line – a line that is added to a figure to aid in a proof. Corollary – a theorem whose proof follows directly from another theorem Interior angle – Formed by two sides of a triangle Exterior Angle - Formed by one side of the triangle and extensions of an adjacent side Third Angles Theorem – If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. Exterior Angle Theorem – The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Triangle Sum Theorem – The sum of the angles of a triangle is 180 degrees. Obtuse Triangle – a triangle that contains an obtuse interior angle Acute Triangle – a triangle whose interior angles are all acute Right Triangle – a triangle with a right angle, otherwise known as a 90 degree angle.

  5. Corollaries The acute angles of a right triangle are complementary. The measure of each angle of an equiangular triangle is 60 degrees.

  6. Geometry Chapter Three Test What postulate or postulates prove these triangles congruent? 2.

  7. Geometry Chapter Three Test 3. 4.

  8. Geometry Chapter Three Test 5. 6. Given triangle JKL is congruent to triangle QRS complete each statement below. a. What is segment JK congruent to? b. What is angle Q congruent to ? c. What is angle SRQ congruent to? d. What is angle KLJ congruent to?

  9. Geometry Chapter Three Test For 7-8 use the triangle ABC below. 7. What is the value of Angle C? 8. What type of triangle is this?

  10. Geometry Chapter Three Test For 9-15State the theorem or triangle definition described. 9.What type of triangle has only two congruent sides? 10. If two angles and an included side of one triangle are congruent to two angles and an included side of another triangles, the triangles are congruent. 11. If the hypotenuse and legs of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. 12. A triangle that has at least one angle larger than 90 degrees. 13. The sum of the angle measure of a triangle is 180 degrees. 14. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. 15. If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent.

  11. Geometry Chapter Three Test Answer Key • HL Theorem; SAS Postulate • ASA Postulate • SSS Postulate; SAS Postulate • ASA Postulate • AAS Theorem • Segment QR • Angle J • Angle LKJ • Angle RSQ • 26 degrees

  12. Geometry Chapter Three Test Answer Key Obtuse Triangle Isoscles Triangle ASA Postulate HL Theorem Obtuse Triangle Triangle Sum Theorem Triangle Inequality Postulate SSS Postulate

  13. BIANCO MATH BIANCOMATH.COM

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