spi 3108.4.3 identify, describe and/or apply the relationships and theorems involving different...
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SPI 3108.4.3 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
A B
a
b
c
An acute triangle is a triangle with all acute angles. An acute triangle has three angles each less than 90 degrees.
80
50 50
An obtuse triangle is a triangle with one obtuse angle (greater than 90 degrees) and two acute angles.
11030
40
A right triangle is a triangle with one right angle (equal to 90 degrees) and two acute angles.
90
45
45
A scale triangle is a triangle with three unequal sides.
12 9
18
An isosceles triangle is a triangle with (at least) two equal sides.
12
14 14
The Isosceles Triangle Theorem states if two sides of a triangle are congruent, then the angles opposite those sides are congruent.
12
14 14
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
Leg
Hypotenuse
For a right triangle with legs a and b and hypotenuse c, a2
+ b2 = c2. ca
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) r2
B) (a+b)2/2=c C) a2+b2=c2
Answer: C) a2+b2=c2
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
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