FTCE Middle Grades Math 5-9
Angles
Competency 8
Angle pairs formed when two parallel lines are cut
by a transversal
Complementary angles – add up to 90
1
3
5
7
2
4
6
8
Corresponding Angles - angles at the same location
at each intersection. (Congruent)
Supplementary angles – add up to 180
∠1 and ∠5
∠3 and ∠7
∠2 and ∠6
∠4 and ∠8
Alternate Interior Angles - two interior angles
which lie on different parallel lines and on opposite
sides of a transversal. (Congruent)
∠4 and ∠5
Adjacent angles – have a common vertex and share
a side
∠3 and ∠6
Alternate Exterior Angles - two exterior angles
which lie on different parallel lines and on opposite
sides of a transversal. (Congruent)
∠1 and ∠8
∠2 and ∠7
Lines
Parallel lines – two coplanar lines that do not
intersect (they have the same slope.
Vertical angles – angles opposite each other when
two lines cross. (Congruent)
Perpendicular lines – two lines that intersect to form
right angles (slopes are negative reciprocals of each
other.
Skew lines – two noncoplanar lines that do not
intersect.
FTCE Middle Grades Math 5-9
Competency 8
Classifying Triangles
Properties of Congruence
Sides
Reflexive Property
A quantity is congruent (equal) to itself. a ≅ a
Equilateral – three congruent sides
Symmetric Property
If a ≅ b, then b ≅ a.
Transitive Property
If a ≅ b and b ≅ c, then a ≅c.
Isosceles – at least two congruent sides
Sum of the measures of the interior angles of a
polygon:
180°(n-2)
Base angles are ≅
n = the number of sides of the polygon
Scalene – no congruent sides
Measure of each interior angles of a regular
polygon:
180°(n-2)
n
Angles
Sum of the measures of the exterior angles of a
polygon = 360
Acute – three acute angles
Triangle Inequality Theorem
The sum of the lengths any two sides of a triangle
must be greater than the length of the third side.
Right - one right angle
a+b>c
b+c>a
a+c>b
Triangle Inequalities – in a triangle the largest angle
is opposite the longest side and the smallest angle is
opposite the shortest side.
Obtuse – one obtuse angle
FTCE Middle Grades Math 5-9
Pythagorean Theorem
Competency 8
Special Right Triangles
a2 + b2 = c2
45° - 45° - 90°
Triangle Congruency Theorems
30° - 60° - 90°
Right Triangle Trigonometry
“SOHCAHTOA”
Similar Figures - Corresponding angles are
congruent and corresponding sides are proportional.
10 12 5
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20 24 10