Tangents & Tangent Angles Ms. “G”

Have you heard of the expression: “going off on a tangent”?

TODAY: we will be exploring the properties of tangents and angles formed by tangents.

TEAMWORK Suppose your seats in the football stadium are further back in the Level 7 seating above the Bull Gator Deck. Complete your “TANGENTS” worksheets in groups of 4 pairs Follow the directions on your handout using rulers, and protractors

PART ONE: FIRST: draw 2 lines: one from your seat to point A, and the other from your seat to point B SECOND: Draw the radius!! Of the circle to points A and B THIRD: measure the angle formed by the radius and tangent line…RECORD! FOURTH: Measure the length of the tangent line segments SA and SB…RECORD!

PART TWO What if you are sitting somewhere behind the end zone marked by point E. FIRST: draw the tangent lines from your seat E to points A and D SECOND: draw the radius to points A and D THIRD: measure the angle formed between tangent line and radius…RECORD! FOURTH: measure the length of the tangent line segments EA and ED…RECORD

What can we conclude from these observations? What do all tangent lines have in common when the radius of the circle is drawn to the point of tangency? Can you draw a tangent line that does not form a right angle with the radius?   What can we conclude from these observations?

WRITE THIS DOWN & STAR IT  a line is tangent if it is perpendicular to the radius drawn to the point of tangency

What can we conclude from these observations? What were the tangent line segment lengths? What did the congruent ones have in common? What can we conclude from these observations?

WRITE THIS DOWN & STAR IT  2 tangents from the same exterior point are congruent

TEAMWORK: “Tangent Angles” Draw a set of tangent lines that intersect in an angle outside your circle Measure the angle the tangent lines create Draw a central angle whose endpoints are the points of tangency Measure this angle to find the measure of the major and minor arcs and record in chart Repeat steps 1-4 for 3 different sets of tangent lines

What do you notice about the angle measure and the arc measures? Is there a relationship between them?

CHALLENGE: create a formula for calculating tangent angle measure using its arc measures

WRITE THIS DOWN & STAR IT  the measure of the angle created by two tangent lines is ½(arc length of the major arc-arc length of minor arc) Angle= ½(major arc-minor arc)