Lesson Plan for High School Geometry · 2018-09-04 · Lesson Plan for High School Geometry Lesson: Points of Concurrency of Triangles South Carolina Standards: G.GCO.11* Construct

Lesson Plan for High School Geometry Lesson: Points of Concurrency of Triangles South Carolina Standards: G.GCO.11* Construct geometric figures using a variety of tools, including a compass, a straightedge, dynamic geometry software, and paper folding, and use these constructions to make conjectures about geometric relationships. G.GCO.8* Prove, and apply in mathematical and real-world contexts, theorems about lines and angles, including that any point on a perpendicular bisector of a line segment is equidistant from the endpoints of the segment. Objective: Students will discover characteristics of points of concurrency for different constructions and different types of triangles. Essential Questions:

• How can I find the points of concurrency for a triangle? • What is unique about each point of concurrency?

Time frame: This entire lesson will take two 90-minute class periods. Lesson Plan: Day 1: • Students will discover the properties of the points of concurrency for different constructions

(perpendicular bisectors, angle bisectors, medians, and altitudes). Students will also discover where the point of concurrency occurs, depending on the type of triangle (acute, right, or obtuse).

• Construction Packet (see below) o Construction Packet Answer Key for the teacher (see below)

• Brief wrap up for the lesson: Watch the YouTube video by Candy Reynolds: https://www.youtube.com/watch?v=zn1xh_asz0E

Day 2: • Watch the “Review of Triangle Properties” video from Khan Academy as a brief review:

https://www.khanacademy.org/math/geometry-home/triangle-properties/triangle-property-review/v/review-of-triangle-properties

• Students should try to complete the notes on “Points of Concurrency” (see below) on their own as a review.

o “Points of Concurrency” Answer Key (see below) • Students should work in pairs to sketch the possibilities for each point of concurrency on the

“Special Segments in Triangles” (see below) page. o Special Segments in Triangles Answer Key (see below)

Informal Assessment: • Students will be constantly monitored as they construct points of concurrency.

Errors/problems will be addressed as they occur. • Terms will be constantly reinforced by the teacher as the students work through the

constructions packet and worksheets. All needed worksheets/packets are below. The order of the items is:

• Construction packet • Construction packet answer key • Notes on “Points of Concurrency” • “Points of Concurrency” answer key • “Special Segments in Triangles” • “Special Segments in Triangles” answer key

Geometry Name _________________________ Points of Concurrency When three of more lines (rays or segments) intersect in the same point, they are called concurrent lines. The point of intersection of these lines is called the point of concurrency. There are four points of triangle concurrency, depending on which segments are drawn:

• Perpendicular Bisectors – Circumcenter o Constructed by ____________________________________________ o _______________________________________________________. o It is equidistant from the __________ of the triangle. o It lies ______________ the triangle when the triangle is ___________. o It lies ______________ the triangle when the triangle is ___________. o It lies ______________ the triangle when the triangle is ___________.

• Angle Bisectors – Incenter o Constructed by ____________________________________________ o _______________________________________________________. o It is equidistant from the __________ of the triangle. o The incenter of a triangle always lies ______________ the triangle.

• Medians – Centroid o Constructed by ____________________________________________ o _______________________________________________________. o The centroid of a triangle always lies ______________ the triangle. o What is unique about the centroid?

• Altitudes – Orthocenter o Constructed by ____________________________________________ o _______________________________________________________. o It lies ______________ the triangle when the triangle is ___________. o It lies ______________ the triangle when the triangle is ___________. o It lies ______________ the triangle when the triangle is ___________.

How can I remember this vocabulary?

All Of Altitude – Orthocenter My Children Median – Centroid Are Bringing In Angle Bisector – Incenter Peanut Butter Cookies Perpendicular Bisector – Circumcenter

Special Segments in Triangles Special

Segment Definition Point of

Concurrency Acute Triangle Obtuse Triangle Right Triangle

Perpendicular

Bisector

Angle Bisector

Median

Altitude