Honors Geometry

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Oct 10, 2013 (4 years and 2 days ago)

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Honors Geometry

Learning Goals


Chapter 1


Points, Lines, Planes, and Angles

Learning Goals

Use the terms
equidistant, point,
and

line.

(1
-
1)

Draw representations of points and lines. (1
-
1)

Use the undefi
ned terms
point, line,
and

plane.

(1
-
2)

Draw representations of points, lines, and planes (1
-
2)

Use the terms
collinear, coplanar,
and
intersection.
(1
-
2)

Use symbols for lines, segments, rays, and distanc
es. (1
-
3)

Find distances. (1
-
3)

State and use the Ruler Postulate and the Segment Addition Postulate (1
-
3)

Name angles and find their measures. (1
-
4)

State and use the Angle Addition Postu
late (1
-
4)

Recognize what can be concluded from a diagram. (1
-
4)

Use postulates and theorems relating points, lines, and planes. (1
-
5)



Chapter 2


Deductive Reasoning

Learning Goals

Recognize the hypothe
sis and the conclusion of an if
-
then statement. (2
-
1)

State the converse of an if
-
then statement. (2
-
1)

Use a counterexample to disprove an if
-
ten statement (2
-
1)

Understand the meaning of
if and only if
.
(2
-
1)

Use properties from Algebra and properties of congruence in proofs. (2
-
2)

Use the Midpoint Theorem and the Angle Bisector Theorem. (2
-
3)

Know the kinds of reasons that can be used in proofs. (2
-
3)

Apply the definitions of complementary and supplementary angles. (2
-
4)

State and use the theorem about vertical angles. (2
-
4)

Apply the definitions and theorems about perpendicular lines. (2
-
5)

State and apply the theorems about angles supplementary to, or complementary to,

congruent angles. (2
-
6)

Plan proofs and then write them in two
-
column form. (2
-
6)

Chapter 3


Parallel Lines and Planes

Learning Goals

Di
stinguish between intersecting lines, parallel lines, and skew lines. (3
-
1)

State and apply the theorem about the intersection of two parallel planes by

a third plane. (3
-
1)

Identify the angles formed when two lines are c
ut by a transversal. (3
-
1)

State and apply the postulates and theorems about parallel lines. (3
-
2 and 3
-
3)

State and apply the theorems about a parallel and a perpendicular to a given line

through a point outside the line.

(3
-
3)

Classify triangles according to sides and to angles. (3
-
4)

State and apply the theorems and the corollaries about the sum of the measures

of the angles of a triangle. (3
-
4)

State and apply the theo
rem about the measure of an exterior angle of

a triangle. (3
-
4)

Recognize and name convex polygons and regular polygons. (3
-
5)

Find the measures of interior angles and exterior angles of convex polygons. (3
-
5)

Understand and use inductive reasoning. (3
-
6)


Chapter 4


Congruent Triangles

Learning Goals

Identify corresponding parts of congruent figures. (4
-
1)

Prove two triangles congruent by using the SSS, SAS, and ASA Post
ulates. (4
-
2)

Deduce information about segments and angles after proving that two triangles are
congruent. (4
-
3)

Apply the theorems and corollaries about isosceles triangles. (4
-
4)

Use the AAS Theorem to p
rove two triangles congruent. (4
-
5)

Use the HL Theorem to prove two right triangles congruent. (4
-
5)

Prove that two overlapping triangles are congruent. (4
-
5)

Prove two triangles congruent by first proving

two other triangles congruent. (4
-
6)
Apply the definitions of the median and the altitude of a triangle and the

perpendicular bisector of a segment. (4
-
7)

State and apply the theorem about a point on the perpendicular bi
sector of a

segment, and the converse. (4
-
7)

State and apply the theorem about a point on the bisector of an angle,

and the converse. (4
-
7)


Chapter 5


Quadrilaterals

Learning Goals

Apply the definition of a parallelogr
am and the theorems about properties

of a parallelogram. (5
-
1)

Prove that certain quadrilaterals are parallelograms. (5
-
2)

Apply theorems about parallel lines. (5
-
3)

Apply the midpoint theorems for triang
les. (5
-
3)

Apply the definitions and identify the special properties of a rectangle, a rhombus,

and a square. (5
-
4)

Determine when a parallelogram is a rectangle, rhombus, or square. (5
-
4)

Apply the defin
itions and identify the properties of a trapezoid and an

isosceles trapezoid. (5
-
5)


Chapter 6


Inequalities in Geometry

Learning Goals

Apply properties of inequality to positive numbers, lengths of segments,

and measures of angles. (6
-
1)

State and use the Exterior Angle Inequality Theorem. (6
-
1)

State the contrapositive and inverse of an if
-
then statement. (6
-
2)

Understand the relationship between logically equivalent statements. (6
-
2)

Draw correct conclusions from given statements. (6
-
2)

Write indirect proofs in paragraph form. (6
-
3)

State and apply the inequality theorems and corollaries for one triangle. (6
-
4)

State a
nd apply the inequality theorems for two triangles. (6
-
5)