Lines, Angles, and Triangles – Part B 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.

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