Download Advanced Geometry 2 Semester Study Guide

Advanced Geometry 2nd Semester Study Guide
Unit 4: Triangle Congruence
4.1
Determine and justify that two triangles are congruent using congruence theorems

What are congruent triangles?

Use the definition of congruence in terms of rigid transformations to determine whether 2
figures are congruent and describe the sequence of rigid motions
o Reflection, Rotation, Translation

Write a congruence statement (order matters!)

Determine if triangles are congruent (SSS, SAS, ASA, AAS Theorems) (Not SSA!!)
o Other definitions/theorems that help:
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4.2

Isosceles Triangle Defintion/Theorem
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Reflexive Property
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Midpoint Theorem
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Definition of Segment/Angle Bisector
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Parallel Line Theorems (AIA, Corresponding Angles, SSIA, AEA)
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Vertical Angle Theorem
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Definition of Equilateral Triangle
Proofs!
Solve Problems involving congruent triangles and corresponding parts

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
o When do we use it? (What must be shown first?)

Use a congruence statement to match the corresponding parts of the triangles

Proofs!
Unit 5: Similarity
5.1
Identify similar triangles and use proportions and triangle properties to solve and justify
solutions to problems

What are similar triangles?
o Angles are ______________
o Sides are _________________

Write a similarity statement (order matters!)

Determine if triangles are similar (AA~, SSS~, SAS~)
o Be sure to check to see if sides are proportional!

Set up and solve proportions
o Big triangle/little triangle
o Triangle Proportionality Theorem
o 3 parallel lines with 2 transversals
o Angle bisector proportionality

Triangle Midsegment Theorem
o What is a midsegment?
o How does it relate to the side of the triangle it doesn’t intersect
5.2
Determine and apply scale factor

Find scale factor (of – top, to – bottom)
o Enlargement: Scale Factor > ____
o Reduction: Scale Factor < ____

Dilations – What is it?
o Find the center of dilation
o Find the scale factor
5.3
Identify similar right triangles formed by the altitude drawn to the hypotenuse and use those
properties to solve problems
𝑎
𝑥

Geometric Mean: 𝑥 = 𝑏, x is the geometric mean of a and b

What is an altitude?

A right triangle with an altitude drawn to the hypotenuse forms 3 similar triangles
o Write a similarity statement for them
o Write 3 different proportions

Legs and altitude are geometric means

Parts of the hypotenuse are the a and b
Unit 6: Right Triangle Relationships and Trigonometry
6.1
Use Pythagorean Theorem to identify and justify relationships in triangles and apply
relationships in problems involving right triangles

Simplify square roots

Pythagorean Theorem
o What is it?
o What must be true before you can use it?

Special Right Triangles
o 45-45-90: What is the rule?

o 30-60-90: What are the rules?


6.2
Solve right triangles and application problems using trigonometric ratios

Trig ratios:
o How do you remember the pattern?
o What do you use to find missing angles?

Word problems:
o Angles of elevation/depression: where are they?
o Eye level problems: how does it affect the problem?
Unit 7: Quadrilaterals
7.1
Solve application problems involving the properties of quadrilaterals

How do you name quadrilaterals

Sum of the angles of a quadrilateral:

Study the family tree or table of characteristics

Properties of Parallelograms:
o
o
o
o
o

Properties of Rectangles: (all properties of parallelograms +)
o
o

Properties of Rhombi: (all properties of a parallelogram +)
o
o
o

Properties of Squares:

Property of Trapezoids:
o Isosceles Trapezoids:


o Midsegment:

Properties of Kites:
o
o
o
o
o
7.2
Identify quadrilaterals on a coordinate plane, and justify the identification using the appropriate
tools and methods

Determine what type of quadrilateral is formed by 4 points
o Slope Formula:

How does it help?
o Distance Formula:

How does it help?
o Midpoint Formula:

How does it help?

4 ways to test for a parallelogram:

2 ways to test for a rectangle:

2 ways to test for a rhombus:

Test for a trapezoid (isosceles?):

If no parallel sides, how do you test for a kite: