Geometry Quarter 2 ( October 11-December 16,2022 ) Scope & Sequence for SY 2022-2023:
CONGRUENT TRIANGLES USING SSS, SAS, ASA, & AAS POSTULATES
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
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
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
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.
MP 1, MP 3 MP 4, MP 6
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