Illustrative Mathematics - Geometry - Unit 7 - Lesson 10

Here are 2 circles. The smaller circle has radius r, circumference c, and diameter d. The larger circle has radius R, circumference C, and diameter D. The larger circle is a dilation of the smaller circle by a factor of k.Using the circles, write 3 pairs of equivalent ratios. Find the value of each set of ratios you wrote.

Tags

G.SRT.1.b

G.GMD.1

G.SRT.1.a

G.C.5

G.C.1

Tyler is confident that all circles are similar, but he cannot explain why this is true. Help Tyler explain why all circles are similar.

Tags

G.SRT.1.b

G.GMD.1

G.SRT.1.a

G.C.5

G.C.1

Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and calculates the arc length to be 4\pi inches. Whose paper is larger? Explain or show your reasoning.

Tags

G.SRT.1.b

G.GMD.1

G.SRT.1.a

G.C.5

G.C.1

A circle has radius 3 centimeters. Suppose an arc on the circle has length 4\pi centimeters. What is the measure of the central angle whose radii define the arc?

Tags

G.SRT.1.b

G.GMD.1

G.SRT.1.a

G.C.5

G.C.1

Chords AC and DB intersect at point E. Select all pairs of angles that must be congruent.

• {"blocks":[{"key":"1a4r4","text":"angle ADB and angle ACB","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":3,"style":"BOLD"},{"offset":20,"length":3,"style":"BOLD"},{"offset":6,"length":3,"style":"ITALIC"},{"offset":20,"length":3,"style":"ITALIC"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"5g19b","text":"angle ADB and angle CAD","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":3,"style":"BOLD"},{"offset":20,"length":3,"style":"BOLD"},{"offset":6,"length":3,"style":"ITALIC"},{"offset":20,"length":3,"style":"ITALIC"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"dpbtc","text":"angle DEA and angle CEB","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":3,"style":"BOLD"},{"offset":20,"length":3,"style":"BOLD"},{"offset":6,"length":3,"style":"ITALIC"},{"offset":20,"length":3,"style":"ITALIC"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"6afaq","text":"angle CAD and angle CBD","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":3,"style":"BOLD"},{"offset":20,"length":3,"style":"BOLD"},{"offset":6,"length":3,"style":"ITALIC"},{"offset":20,"length":3,"style":"ITALIC"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"3tp7","text":"angle BCA and angle CBA","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":3,"style":"BOLD"},{"offset":20,"length":3,"style":"BOLD"},{"offset":6,"length":3,"style":"ITALIC"},{"offset":20,"length":3,"style":"ITALIC"}],"entityRanges":[],"data":{}}],"entityMap":{}}

Tags

G.SRT.1.b

G.GMD.1

G.SRT.1.a

G.C.5

G.C.1