• Geometry Quarter 2 ( October 11-December 16,2022 ) Scope & Sequence for SY 2022-2023:

CONGRUENT TRIANGLES USING SSS, SAS, ASA, & AAS POSTULATES

AZMathematics Standards:

G-SRT.B.5 : Use congruence ....criteria for triangles to solve problems and prove relationships in geometric figures.

Mathematical Practices:  MP 1, MP 3, MP 4, MP 7

Lesson Objective: To prove triangles congruent using SSS, SAS, ASA, & AAS Postulates.

Postulate 1: Sise-Side-Sisde ( SSS) Postulate

If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Postulate 2: Sise-Angle-Side (SAS) Postulate

If two sides and the included angle of one triangle are congruent to two sides aand the included angle of anothet triangle, then the two triangles are congruent.

Postulate 3:  Angle-Side-Angle ( ASA) Postulate

If two angles and the included side of one triangle are congruent ot two sides and the included side of another triangle, then the two triangles are congrunet.

Postulate 4: Angle-Angle -Side (AAS) Theorem

If two angles and a nonincluded side of one trisngle ar congruent to two angles and the corresponding side of another triangle, then the two triangles are congruent.

STEPS or LESSON PROCEDURES:

1. PLAN   :   ex. You have two pairs of congruent sides, what else do you need? Use the Study Guide to understand    the concepts.

2. THINK :   Vocabulary words : congruent, corresponding, included angle or included side , ex. Can you eliminate any of the choices?

3.APPLY  :    Use Postulate or Theorem to prove two triangles congruent, like SSS, SAS, ASA or AAS.

AZMath Standards:  G-GPE.B.4 : Use coordinates  to prove simple geometric Theorems...

G-GPE. B.7: Use coordinates to compute perimeters... and areas...

G-CO.C.10  Prove Theorems about triangless...the medians of a triangle meet at a point.

Mathemarical Practices: MP 1, MP 3, MP 4

lesson Objectives:

a. To find the midpoint  of a segment

b. To find the distance between two points in the coordinate plane

c. To identify properties of medians and Altitudes of a triangle

Steps or Lesson Procedures:

1. Plan     : How do you detemine whether a segment is an altitude or a median?

2. Think   : Which two altitudes should you use? Use vocabulary here: like centroid, median, altitude, orthocenter

3. Apply   :  Use Theorem 5-8 : Concurency of Medians Theorem

4. continue doing work in medians & altitudes , Midpoint of segments

RIGHT TRIANGLES, PYTHAGOREAN THEOREM, SPECIAL RIGHT TRIANGLES, TRIGONOMETRY

AZMath Standards: G- SRT.C.8 : use .... the Pythagorean Theorem to solve right triangles in applied problems.

Mathematical Practices:   MP 1, MP 3,  MP 4, MP 6

lesson Objectives:

a. To use Pythagorean Theorem  and its converse

b. To use  the properties of 45-45-90 and 30-60-90 triangles

c. To use the sine, cosine, and tangent ratios to determine side lenghts and angle memasures in right triangles

Steps or lesson Procedures:

a. PLAN    : How do you know where each of the side lenghts goes in the equation?

b THINK   : How do you know that d is th hypotenus? Vocabulaty words: hyponetune, Pythagorean Theorem,

c. APPLY  : What Theorem is applied to find the missing side or missing angle of a right triangle? Write the equation.

d. CONTINUE doing your APEX work now.

AZ MATH STANDARDS:

G-CO.C.11:     Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles

are congruent, the diagonals of a parallelogram bisect each other.

G- GPE. B.4 :  Use coordinates to prove simple geometric theorems algebraically.

Mathematical Practices:  MP 1, MP 3, MP 4

LESSON OBJECTIVES:

a. To use relationships among sides and angles of parallelograms

b. To use relationships among diagonals of parallelograms

c. To detemine whtether a quadrilateral is a parallelogram

d. To verify and use properties of trapezoids ans kites

e. To name coordinates of special figures by using their properties

STEPS OR LESSON PROCEDURES:

a. PLAN     : What information from the diagram helps you get started?

b. THINK   :  Why is a flow proof useful here? What do you know about the angles of an isosceles trapezoid?

c. APPLY   :   Which teorem should you use here? How do you check your answer?

d. CONTINUE: Your Turn to do Assignments NOW.

CIRCLES WITHOUT COORDINATES

AZ Math STANDARDS :

G.C.A. 2 :  Identify and describe relationships among incribed angles, radii, and  chords .... the radius of

a circle is perpendicular to the tangent where the radius intrsects the circle.

MATHEMATICAL PRACTICES:

MP 1, MP 3 MP 4, MP 6

LESSON OBJECTIVES:

a. To use properties of a tangent of a circle

b.  to find the measure of an inscribed angle

c. To find the measure of an angle formed by a tangent and a chord

d. To find the circumference and areas of circles

# APEX Q2 Due Dates

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