Download Honors/Standard Geometry Pacing Guide 2016

Honors/Standard Geometry
Pacing Guide 2016-2017
Quarter 2
Unit 4: Congruent Triangles
Standards
Week
Week 10
Oct. 18-21
(4 days)
District PD
G.T.1: Prove and apply theorems about triangles, including the following: 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; a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem, using triangle similarity; and the isosceles triangle theorem and its converse.

Classify triangles based on properties. Use properties of sides and angles to find missing measurements.
G.T.2: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Develop and use Triangle Congruence theorems.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.T.1: Prove and apply theorems about triangles, including the following: 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; a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem, using triangle similarity; and the isosceles triangle theorem and its converse.

Continue using properties of triangles create new proofs, students should be justifying their arguments.
G.T.2: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Continue using Triangle Congruence Theorems.
Week 11
Oct. 24-28
G.T.3: Explain and justify the process used to construct congruent triangles with a variety of tools and methods (compass and straightedge, string, reflective devices, paper
folding, dynamic geometric software, etc.).

Construct triangles that are congruent to given triangles.
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs,
and flow charts formats.

Use proof method of choice.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.T.1: Prove and apply theorems about triangles, including the following: 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; a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem, using triangle similarity; and the isosceles triangle theorem and its converse.

Use theorems and properties of isosceles and equilateral triangles to guide this week.
Week 12
Oct. 31-Nov 4
G.T.2: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Review and use as necessary
G.T.3: Explain and justify the process used to construct congruent triangles with a variety of tools and methods (compass and straightedge, string, reflective devices, paper
folding, dynamic geometric software, etc.).

Review and use as necessary
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs,
and flow charts formats.

Review and use as necessary
Indianapolis Public Schools
Curriculum and Instruction
Honors/Standard Geometry
Pacing Guide 2016-2017
Quarter 2
G.PL.5: Explain and justify the process used to construct, with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
geometric software, etc.), congruent segments and angles, angle bisectors, perpendicular bisectors, altitudes, medians, and parallel and perpendicular lines.

Explore congruencies using manipulatives and develop new theorems or justify previous theorems.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.T.1: Prove and apply theorems about triangles, including the following: 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; a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem, using triangle similarity; and the isosceles triangle theorem and its converse.

Use transformations on coordinate grids to explore congruencies.
Week 13
Nov. 7-11
G.T.2: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Demonstrate an understanding on a coordinate grid
G.LP.1: Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and
theorems). Understand the differences among supporting evidence, counterexamples, and actual proofs.

Have students determine what counts as proofs when using coordinate grids as a guide, what is supporting evidence, and how counterexamples can be drawn.
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs,
and flow charts formats.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Unit 5: Relationships With Triangles
Week
Standards
Benchmark 2 Window Opens-
10th
grade only
G.LP.1: Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and
theorems). Understand the differences among supporting evidence, counterexamples, and actual proofs.

Review and further develop the idea of proof and argument using supporting evidence, counterexamples, and formal proofs.
Week 14
Nov. 14-18
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs,
and flow charts formats.

Use proof method of choice.
G.T.3: Explain and justify the process used to construct congruent triangles with a variety of tools and methods (compass and straightedge, string, reflective devices, paper
folding, dynamic geometric software, etc.).

Construct circumcenters, centroids, orthocenters, and incenters
G.PL.3: Prove and apply theorems about lines and angles, including the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior
angles are congruent, alternate exterior angles are congruent, and corresponding angles are congruent; when a transversal crosses parallel lines, same side interior angles are
supplementary; and points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the segment.

Develop and use bisectors, medians, and altitudes of triangles.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Week 15
Nov. 21 & 22
(2 days)
Benchmark 2 Window Closes
G.T.1: Prove and apply theorems about triangles, including the following: 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; a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem, using triangle similarity; and the isosceles triangle theorem and its converse.
Indianapolis Public Schools
Curriculum and Instruction
Honors/Standard Geometry
Pacing Guide 2016-2017
Quarter 2
Thanksgiving
Break
Week 16
Nov. 28 – Dec. 2
Week 17
Dec. 5 - 9
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Corrective Instruction – based on data from Benchmark 2 and other formative assessments
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.T.1: Prove and apply theorems about triangles, including the following: 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; a line parallel to one side of a
triangle divides the other two proportionally, and conversely; the Pythagorean Theorem, using triangle similarity; and the isosceles triangle theorem and its converse.

Continue this standard as necessary
G.T.6: Prove and apply the inequality theorems, including the following: triangle inequality, inequality in one triangle, and the hinge theorem and its converse.

Develop and use triangle inequality theorems.
G.T.7: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. Understand and use the geometric mean to solve for
missing parts of triangles.
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs,
and flow charts formats.

Develop indirect proofs
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Week 18
Dec. 12 - 15
Post-Test
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Process Standards for Mathematics (PS):
1. Make sense of problems
and persevere in solving
them.
2. Reason abstractly and
quantitatively.
3. Construct viable
arguments and critique the
reasoning of others.
4. Model with
mathematics.
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use
of structure.
WINTER BREAK
Dec. 19-Jan. 2
End of First Semester
Indianapolis Public Schools
Curriculum and Instruction
8. Look for and express
regularity in repeated
reasoning.