Download Subject Geometry Academic Grade 10 Unit # 2 Pacing 8

Subject
Geometry
Academic
Grade
10
Unit #
2
Pacing
8-10 weeks
Triangles and Quadrilaterals
Unit Name
Overview
In Unit 2 students will thoroughly study the properties of triangles. Students will be able to identify congruent triangles, write congruence
statements, and apply theorems to prove triangles congruent. Students will also study the properties of quadrilaterals and be able to
identify the different quadrilaterals by their sides and angles. The unit will also have students investigate properties of triangles and
quadrilaterals on the coordinate plane. Students will identify figures and find perimeters using algebraic concepts.
Standard #
Standard
MC,
SC,
or
AC
Prove theorems about triangles. Theorems
include: measures of interior angles of a triangle
sum to 180°; base angles of isosceles triangles
are congruent; the segment joining midpoints of
two sides of a triangle is parallel to the third side
and half the length; the medians of a triangle
meet at a point.
G.CO.10
MC
SLO
#
Student Learning Objectives
Depth of
Knowledge
1
2
3
4
5
6
7
8
9
Apply the Triangle Angle Sum Theorem
Apply the Third Angle Theorem
Apply the Exterior Angle Theorem
Apply the Angle, Angle, Side Congruency Theorem
Apply the Isosceles Triangle Theorem
Apply the Converse of the Isosceles Triangle Theorem
Apply the Triangle Midsegment Theorem
Apply the Exterior Angle Inequality Theorem
Apply the fact that the side opposite the greater angle in a
triangle is longer than the side opposite the lesser angle,
and the converse of these relationships
Prove that the perpendicular segment from a point to a line
is the shortest segment (distance) from the point to the line
Apply the Triangle Inequality Theorem
Apply the Side Angle Side Inequality Theorem
Apply the Side, Side. Side Inequality Theorem
4
Apply rigid motion arguments to show that two triangles
are congruent
Apply rigid motion arguments to show that two geometric
figures are congruent
Prove two triangles congruent using the SSS Theorem
4
10
11
12
G.CO.7
G.CO.8
Use the definition of congruence in terms of rigid
motions to show that two triangles are congruent
if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent
Explain how the criteria for triangle congruence
13
MC
MC
14
15
4
16
17
18
19
20
(ASA, SAS, and SSS) follow from the definition
of congruence in terms of rigid motions
G.CO.13
Construct an equilateral triangle, a square, and
a regular hexagon inscribed in a circle
G.CO.11
Prove theorems about parallelograms.
Theorems include: opposite sides are
congruent, opposite angles are congruent, the
diagonals of a parallelogram bisect each other,
and conversely, rectangles are parallelograms
with congruent diagonals
SC
MC
21
22
23
24
25
26
27
28
29
Use congruence and similarity criteria for
triangles to solve problems and to prove
relationships in geometric figures
G.SRT.5
30
MC
31
G.GPE.4
Use coordinates to prove simple geometric
theorems algebraically. For example, prove or
disprove that a figure defined by four given
points in the coordinate plane is a rectangle;
prove or disprove that the point (1, √3) lies on
the circle centered at the origin and containing
the point (0, 2)
32
MC
33
34
35
G.GPE.7
Big Ideas
Use coordinates to compute the perimeters of
polygons and areas of triangles and rectangles
(e.g using the distance formula)
MC
36
Prove two triangles congruent using the SAS Theorem
Prove two Triangles congruent using the ASA Theorem
Prove two triangles congruent using the AAS Theorem
Prove two triangles congruent using the HL Theorem
Generate formal constructions of regular polygons inscribed
in a circle with paper folding, geometric software or other
geometric tools.
Apply the following facts about parallelograms:
Opposite sides of a parallelogram are congruent
Opposite angles of a parallelogram are congruent
The diagonals of a parallelogram bisect each other
The diagonals of a rectangle are congruent
The fact that the diagonals of a rhombus are perpendicular
The diagonals of a rhombus bisect a pair of opposite angles
A quadrilateral with any one of these properties is a
parallelogram
A quadrilateral has one pair of sides both parallel and
congruent is a parallelogram
Apply congruence and similarity criteria for triangles to
solve problems
Apply congruence and similarity criteria to prove
relationships in geometric figures.
Justify solutions to problems involving side lengths and
angle measures using triangle congruence and similarity
criteria
Prove simple geometric theorems algebraically using the
coordinates of vertices of polygons
Calculate the perimeter and area of figures in the
coordinate plane using the coordinates of the vertices of
geometric figures
Represent geometric figures on a coordinates plane
Calculate the perimeter and area of figures in the
coordinate plane using the coordinates of the vertices of
the figures
Represent geometric figures in the coordinate plane using
the coordinates of the vertices of the figure
4
4
4
4
3
4
3
2
3
2
 Properties of triangles
 Polygon and triangle congruence
 Polygon and triangle similarity
 Parallelograms
Essential questions
What combination of properties will make two triangles similar?
What combination of properties will make two triangles congruent?
What combination of properties will make a quadrilateral a parallelogram?
Key Vocabulary
Isosceles triangles, Equilateral triangles, Equiangular triangles, perpendicular bisector, congruent and similar triangles, similar and congruent triangles, quadrilateral,
parallelogram
Suggested Resources (list specific chapters and or page numbers from existing text that correspond to the SLOs and Standards)
Chapter 4
Chapter 5 (Exclude section 5-4)
Chapter 6