Download Geometry 2nd Semester Final Study Guide

Geometry 2nd Semester Final Study Guide
Chapter 6

Identify medians in triangles
o Connects vertex to midpoint
o Medians meet at the centroid


Centroid is 2/3 of the way along a median
Identify altitudes and perpendicular bisectors in triangles
o Altitude: from vertex to opposite side and perpendicular
o Perpendicular Bisector: Goes through the midpoint of a side, and is perpendicular to that side

Identify and use angle bisectors in triangles
o Goes through the vertex of a triangle, and splits the angle into 2 congruent parts

Identify and use properties of isosceles triangles
o Parts of isosceles triangles: legs, base, base angles, vertex angle
o 2 congruent legs ↔ 2 congruent base angles

Use tests for congruence of right triangles
o LL, HA, LA, HL


What do the H’s, L’s, and A’s stand for?
Use the Pythagorean Theorem and its converse
o If a triangle is a right triangle, then 𝑎2 + 𝑏2 = 𝑐 2 , c is the hypotenuse
o Converse: If 𝑎2 + 𝑏2 = 𝑐 2 , then a triangle is a right triangle

Find the distance between two points on the coordinate plane
o 𝑑 = √(𝑥1 − 𝑥 2 )2 + (𝑦1 − 𝑦2 )2
Chapter 7

Apply inequalities to segment and angle measures
o Inequality symbols: >, <, ≥, ≤, ≠, ≱, ≰
o Be able to compare segments on a number line
o Be able to compare angles in a figure

Identify exterior angles and remote interior angles of a triangle and use the Exterior Angle Theorem
o What is an exterior angle? Remote interior angles?
o Exterior angle = sum of the remote interior angles

Identify the relationships between the sides and angles of a triangle
o Biggest angle across from longest side
o Shortest side across from smallest angle
o Be able to list sides/angles in order when given the angles/sides

Identify and use the Triangle Inequality Theorem
o 2 sides added together > 3rd side
o Find a range of possible values for the 3 rd side of a triangle when given 2 sides

Small end: subtract 2 given sides

Large end: add 2 given sides
Chapter 9

Use ratios and proportions to solve problems
o Always reduce ratios
o Proportions: Cross products are always =

Identify similar polygons
o Same shape, different size
o Angles are congruent
o Sides are proportional

Use AA~, SSS~, and SAS~ similarity tests for triangles
o Check to see if angles are congruent or sides are proportional

Identify and use the relationships between proportional parts of triangles
o Small triangle and big triangle

Use proportions to determine whether lines are parallel to sides of triangles
o If segment in triangle is parallel to the side it doesn’t touch, then set up proportion to find
missing part
o If sides are split proportionally, then line is parallel to side it doesn’t intersect
o Triangle Midsegments – connects midpoints of sides


Parallel to side it doesn’t touch

Half the length of side it doesn’t touch
Identify and use the relationships between parallel lines and proportional parts
o 3 parallel lines crossed by 2 transversals: transversals are split proportionally

Identify and use proportional relationships of similar triangles
o Perimeter can be used just like sides in similar triangles
o Scale Factor: match sides of similar triangles, make a ratio, and reduce

of = top, to = bottom
Chapter 13

Multiply, divide, and simplify radical expressions
o No perfect squares left under √
o No fractions under √
o No √


on the bottom of a fraction
Multiply numerator and denominator by that √
Use the properties of 45-45-90 triangles
o “leg times √ 2 = the hypotenuse”

Use the properties of 30-60-90 triangles
o “shorter leg times 2 = the hypotenuse”
o “shorter leg times √ 3 = the longer leg”

Use the sine, cosine, and tangent ratio to solve problems
o SOH CAH TOA
o Use inverses to find angles
o Angles of elevation/depression
Chapter 8

Identify and use the properties of parallelograms
o Opposite sides are parallel
o Opposite sides are congruent
o Opposite angles are congruent
o Consecutive angles are supplementary
o Diagonals bisect each other

Identify and use tests to show that a quadrilateral is a parallelogram
o Are opposite sides parallel?
o Are opposite sides congruent?
o Are opposite angles congruent?
o Do the diagonals bisect each other?
o Is one pair of opposite sides both parallel and congruent?

Identify and use the properties of rectangles, rhombi, and squares
o Rectangles: All properties of a parallelogram +

4 right angles

Congruent diagonals (forms 4 congruent parts on the diagonals)
o Rhombi: All properties of a parallelogram +

4 congruent sides

Perpendicular diagonals

Diagonals bisect the opposite angles (forms 4 congruent angles across from each other)
o Square: All properties of a parallelogram, rectangle and rhombus
Chapter 10

Name polygons according to the number of sides and angles
o Concave/convex
o Regular polygon – both equilateral and equiangular
o Parts of polygons


Name consecutive/nonconsecutive sides, vertices, angles

Name diagonals
Find measures of interior and exterior angles of polygons
o Interior Angles

Sum of Interior Angles: 𝑆 = (𝑛 − 2)180

Each interior angle of a regular polygon: 𝐼 =
( 𝑛−2) 180
𝑛
o Exterior Angles

Sum of Exterior Angles: always 360° (no matter how many sides)

Each exterior angle of a regular polygon: 𝐸 =
360
𝑛
o Interior Angle + Exterior Angle = 180° (form a linear pair)

Find the areas of triangles and trapezoids
1
o Triangle: 𝐴 = 2 𝑏ℎ
1
o Trapezoid: 𝐴 = 2 (𝑏1 + 𝑏2 )ℎ

Estimate the areas of polygons
o Split irregular polygons into shape you can find the area of
1
o Estimate: Full squares = 1 unit2 , partial squares = unit2
2

Find the areas of regular polygons
o Apothem, a, connects center of polygon to a side and is perpendicular
o Perimeter, P, is the number of sides, n, times the length of each side, s: 𝑃 = 𝑠 ∙ 𝑛
1
o Area: 𝐴 = 2 𝑎𝑃
o Area of shaded region: 𝐴𝑠ℎ𝑎𝑑𝑒𝑑 = 𝐴𝑤ℎ𝑜𝑙𝑒 − 𝐴𝑢𝑛𝑠ℎ𝑎𝑑𝑒𝑑