Geometry Topic 3 Lines Angles and Triangles Part

Geometry Topic 3 Lines, Angles, and Triangles – Part B

Table of Contents • Recommended Instructional Design and Planning Continuum. . . . Slide 3 • Vocabulary …………………………………. . Slides 4 – 16 • Reporting Category Practice Items …………………. Slides 17 - 35

Vocabulary

Mathematically Speaking! Choose 3 -4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods. Examples of accuracy • line vs line segment • translation vs slide • midpoint vs the middle

Equidistant – the same distance from two or more objects.

Distance from a point to a line – the length of the perpendicular segment from the point to the line.

Median of a triangle – a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

Midsegment of a triangle – a segment that joins the midpoints of two sides of the triangle. • The midsegment is always parallel to the third side of the triangle. • The midsegment is always half the length of the third side. • A triangle has three possible midsegments, depending on which pair of sides is initially joined.

Circumscribed circle – every vertex of the polygon lies on the circle.

Inscribed circle – a circle in which each side of the polygon is tangent to the circle.

Point of concurrency – a point where three or more lines coincide. P

Circumcenter of a triangle – the point of concurrency of the three perpendicular bisectors of a triangle. • The circumcenter is also the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices. • The circumcenter is equidistant from all three vertices of the triangle. • In the special case of a right triangle, the circumcenter lies exactly at the midpoint of the hypotenuse.

Centroid of triangle – the point of concurrency of the three medians of a triangle. Also known as the center of gravity. • The centroid is always inside the triangle • Each median divides the triangle into two smaller triangles of equal area. • The centroid is exactly two-thirds the way along each median. The centroid divides each median into two segments whose lengths are in the ratio 2: 1, with the longest one nearest the vertex.

Incenter of a triangle – the point of concurrency of the three angle bisectors of a triangle. • The incenter is the center of the triangle's incircle, the largest circle that will fit inside the triangle and touch all three sides. • The triangle's incenter is always inside the triangle.

Altitude of a triangle – a segment from a vertex perpendicular to the opposite side. Vocabulary for Geometry Honors