Geometry – Chapter 14 Lesson Plans
Section 14.4 – Secant-Tangent Angles
Enduring Understandings: The student shall be able to:
- Find measures of arcs and angles formed by secants and tangents.
Standards:
30. Circles
Identifies and defines circles and their parts (center, arc, interior, exterior); segments and lines associated with circles (chord, diameter, radius, tangent, secant); properties of circles (congruent, concentric, tangent); relationship of polygons and circles (inscribed, circumscribed); angles (central; inscribed; formed by tangents, chords, and secants).
Essential Questions: What is special about Secant-Tangent angles?
Warm up/Opener:
Activities:
A Secant-Tangent Angle is formed when a secant and tangent intersect. This can occur outside of the circle or on the circle.
The rule for finding the measure of the secant-tangent angle when it is outside of the circle is the same as we used for secant angles in section 14-3, namely, the measure of the angle is half the difference of the degree measures of the intercepted arcs.
The rule for finding the measure of the inscribed secant-tangent angle (i.e., the vertex lying on the circle) is the same as the inscribed angles of section 14-1, namely, the measure of the inscribed angle is half the measure of the intercepted arc (or central angle).
A Tangent-Tangent angle is formed by the intersection of two tangents. This angle will always be outside of the circle. The rule for finding the measure of the tangent -tangent angle is also the same as we used for secant angles in section 14-3, namely, the measure of the angle is half the difference of the degree measures of the intercepted arcs.
In summary, to calculate the angle of intersecting lines with a circle:
· If the intersection inscribed (on the circle) take one-half the intercepted arc.
· If the intersection is outside of the circle, take one-half the difference of the intercepted arcs.
· If the intersection is inside of the circle, take one-half the sum of the intercepted arcs.
Assessments:
Do the “Check for Understanding”
CW WS 14.4 and Enrichment 14-4 # 1 - 4
HW pg 610 – 612, # 9 – 27 all (19) if I only cover this section
HW pg 610-612, # 9 - 27 odd (10) if I combine this section with another section
Extra Credit: Enrichment 14-4 # 5 - 8