Download Midterm Exam Review Geometry Know

Name:_________________________________________________
Midterm Exam Review
Date: ___________
Geometry
Know:
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•
•
•
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Formulas:
o Distance Formula (on a number
line and on a coordinate plane)
o Midpoint Formula
o
o
Standard Form of a Line:
Ax + By = C
Slope Intercept Form of a Line:
y = mx + b
Definitions:
o Definition of Adjacent Angles
o Definition of Linear Pair
o Definition of Angle Bisector
o Definition of Midpoint
o Definition of Perpendicular
o Definition of Between
Lines
o Definition of Complementary
Angles
o Definition of Segment Bisector
o Definition of Supplementary
o Definition of Congruence
Angles
(Segments, Angles)
o Definition of Vertical Angles
o Definition of Line Segment
Properties:
o Distributive Property
o Properties Of Congruence: (Reflexive, Transitive, Symmetric) – for Segments, Angles,
and Triangles
o Properties Of Equality: (Addition, Subtraction, Multiplication, Division, Substitution,
Reflexive, Transitive, Symmetric)
o Corresponding Parts of Congruent Figures are Congruent (CPCF)
Postulates:
o Angle Addition Postulate
o Slope of Perpendicular Lines
o Linear Pair Postulate
Postulate
o Segment Addition Postulate
o SSS (Side-Side-Side)
o Corresponding Angles Postulate
Congruence Postulate
o Corresponding Angles Converse
o SAS (Side-Angle-Side)
Postulate
Congruence Postulate
o Slope of Parallel Lines Postulate
o ASA (Angle-Side-Angle)
Congruence Postulate
Theorems:
o Congruent Supplements
o Alternate Exterior Angles
Theorem
Converse Theorem
o Pythagorean Theorem
o Consecutive Interior Angles
o Right Angle Congruence
Converse Theorem
Theorem
o Triangle Sum Theorem
o Vertical Angles Theorem
o Exterior Angle Theorem
o Alternate Interior Angles
o Third Angles Theorem
Theorem
o AAS (Angle-Angle-Side)
o Alternate Exterior Angles
Congruence Theorem
Theorem
o Base Angles Theorem
o Consecutive Interior Angles
o Converse of Base Angles
Theorem
Theorem
o Alternate Interior Angles
o HL (Hypotenuse-Leg)
Converse Theorem
Congruence Theorem
Understand:
• There are two types of geometries: Coordinate (in xy-plane) and Synthetic. In both types
of geometries, all properties, postulates, theorems, and definitions apply because both
geometries are Euclidean. The formulas only apply to Coordinate Geometry.
• We have been focused on 0, 1, and 2-dimensional figures. A point has 0 dimensions. One
dimensional figures include lines, rays, and segments. The only one dimensional figure
that can be measured is a segment. AB notates the measurement of a segment with
endpoints A and B. For angle measure, a small “m” in front of an angle is used to
indicate an angle measure. All figures have a symbol to notate that they are figures and
not measurements. Examples of two dimensional figures (that we have seen a lot of this
semester) are angles, polygons (including triangles), and circles. A one dimensional
measurement can also occur on a two dimensional figure (for example, height of a
triangle or perimeter). Area is a two dimensional measurement.
• Our journey through proofs was:
• Chapter 1: Introduction to notation, geometries, idea of measurement vs. figures
• Chapter 2: Conditional (if-then) statements vs. Biconditional (if and only if)
statements; Postulates (conditionals, cannot be proven) vs. Theorems
(conditionals, can be proven) vs. Definitions (biconditionals, must be proven in
two directions); Segment Addition Postulate vs. Angle Addition Postulate (both
really mean: PART + PART = WHOLE); Properties (used to explain why you
solved equations as you did in algebra); Congruent Complements vs. Congruent
Supplements Theorem
• Chapter 3: Special Pairs of Angles, Theorems and 1 Postulate that allow you to
say special pairs of angles are congruent, Converse Theorems and 1 Converse
Postulate that allow you to say that lines are parallel, Parallel vs. Perpendicular
Lines in a Coordinate Plane
• Chapter 4: Theorems that are always true in triangles (Exterior Angle Theorem,
Triangle Sum Theorem); What it means for two triangles to be congruent;
Congruence justifications that tell you what is just enough to know that triangles
are congruent (ASA, AAS, SSS, SAS, and HL); Using all justifications (theorems,
postulates, properties, and definitions) in proofs; Then finally, using formulas,
congruence statements, and all justifications in proofs in coordinate geometry.
• We took triangles and used them to build polygons. The polygon sum theorem and
regular polygon formulas are not part of the midterm. However, they did help us to
understand the power behind triangles.
• We also investigated what congruent shapes are in coordinate geometry; that they really
are two shapes related by an isometry (translation, rotation, and reflection). The
preimage and image of every isometry are congruent and corresponding parts of those
congruent figures are congruent (CPCF). This idea is not limited to triangles!
Be able to do:
• Identify (notation is important) points, lines, segments, rays, and angles of interest (Are
they part of an intersection? Are they collinear? Are they coplanar or non-coplanar? Are
they a special pair of angles? What name is most applicable? What is the most specific
name for a triangle?)
• Apply formulas (see above)
• Find measures of angles (using information in diagram, algebra, or numerical
relationships)
• Solve for x or y in a diagram
• Given information about a relationship (such as midpoint or bisector) draw a diagram and
solve for x and distances or angle measures
• Compare segments, rays, and lines
• Rewrite a statement in if-then form
• Write the converse of a statement
• Interpret if a statement might be true or false
• Describe what intersections between lines, planes, and/or rays might look like/create
• Find perimeter and area of figures (some may be combined as in a semicircle and a
rectangle; like window)
• Fill in justifications (reasons) of algebraic proof
• Find angle measures in triangles (including exterior angles)
• Decide if two lines are parallel based on given information
• Decide if two triangles are congruent and write a congruence statements
• Fill in justifications (reasons) for a triangle congruence-related proof
• Complete four of five proofs
After finishing the midterm review packets, go back over all quizzes and tests. Look over quiz
and test corrections. You should have no issue going back and efficiently doing these problems.
These problems were designed to simulate the most difficult midterm questions.
The tentative plan:
Friday, 1/20: Chapter 4 Test
Monday 1/23: Corrections in class, questions from midterm review packets 1-2
Tuesday 1/24: Questions from midterm review packets 3-4, including proofs
Wednesday 1/25: Questions from Tests or Quizzes in Chapters 1-4