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GPS Alignment: Instructor Page
Week 10: Geometry - Circles


Angles in a Circle (Printable PDF)

The vertex of an angle can appear on, inside, or outside a circle. How does the location and measure of the vertex angle compare with the measure(s) of the arc(s) it intercepts?
 

     

 

GPS

As seen in Problem Exploration

M6G1. Students will further develop their understanding of plane figures.

b. Demonstrate understanding of similar plane figures and the scale factor between them.
 

The student can use GSP to measure the central angle and the arc lengths to determine a relationship. 

In proving the 3rd case with the angle inside the circle, similar triangles are used to prove the relationship.
 

M7G1. Students will construct plane figures that meet given conditions.
 

Students need to understand what a central angle versus the other angles inside the circle in order to construct the circles and angles correctly.
 

M8G1. Students will analyze and use characteristics and properties of geometric figures.

b.  Use and apply properties of angle pairs such as complementary, supplementary and vertical angles.
 

In proving the cases, the students will use supplementary angles, vertical angles to determine that the various triangles constructed (depending on which case) are either similar or congruent.

M8G2. Students will use the properties of similarity and congruency and apply these concepts to geometric figures.

a.  Understand the meaning of similarity and the conditions for similarity of geometric figures.

c.  Understand the meaning of congruency and the conditions for congruent triangles and other polygons.

d.  Use properties to determine similarity and congruency of triangles.
 

In proving the cases, the students will use supplementary angles, vertical angles to determine that the various triangles constructed (depending on which case) are either similar or congruent.