SPI Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons.

 A triangle is a figure formed by three noncollinear points connected by three segments. All triangles can be classified by it’s side and by it’s angle. C AB a b c

 An acute triangle is a triangle with all acute angles. An acute triangle has three angles each less than 90 degrees

 An obtuse triangle is a triangle with one obtuse angle (greater than 90 degrees) and two acute angles

 A right triangle is a triangle with one right angle (equal to 90 degrees) and two acute angles

 A scale triangle is a triangle with three unequal sides

 An isosceles triangle is a triangle with (at least) two equal sides

 The Isosceles Triangle Theorem states if two sides of a triangle are congruent, then the angles opposite those sides are congruent

 An equilateral triangle is a triangle with all three sides of equal length. Since all three sides are equal; therefore, all three angles are equal also.

 A right triangle has two legs and an hypotenuse. The hypotenuse is the side opposite of the right angle. The other two sides are called legs. Leg Hypotenuse

 For a right triangle with legs a and b and hypotenuse c, a 2 + b 2 = c 2. c a b

 Please complete the following quiz that covers the information that was just presented to you.

 If a triangle has three unequal sides it is a ______ triangle.  A) Scalene  B) Obtuse  C) Isosceles  Answer:  A) Scalene

 A triangle with (at least) two equal sides is a ______ triangle.  A) Scalene  B) Isosceles  C) Congruent  Answer:  B) Isosceles

 A triangle with all three sides of equal length is a ______ triangle.  A) Equilateral  B) Right  C) Equiangular  Answer:  A) Equilateral

 A triangle with an angle of 90° is a ______ triangle.  A) Acute  B) Right  C) Congruent  Answer:  B) Right

 A triangle in which all three angles are less than 90° is a ______ triangle.  A) Right  B) Acute  C) Scalene  Answer:  B) Acute

 A triangle in which one of the angles is greater than 90° is a ______ triangle.  A) Obtuse  B) Isosceles  C) Acute  Answer:  A) Obtuse

 What is the Hypotenuse of a right triangle?  A) The smallest angle.  B) The side opposite the right angle.  C) The right angle.  Answer:  B) The side opposite the right angle.

 The Pythagorean Theorem states …  A)  r 2  B) (a+b) 2 /2=c  C) a 2 +b 2 =c 2  Answer:  C) a 2 +b 2 =c 2

 Use the Pythagorean Theorem to solve the following:  a = 5  b = 12  c = ?  Answer:  c = 13

 Use the Pythagorean Theorem to solve the following:  a = ?  b = 16  c = 20  Answer:  a = 12