Geometry – SpringBoard 2015 Quarter 2 Hunter Smith ESUMS New Haven Public Schools

List of main topics covered on the Quarterly Setting up and solving equations Congruent objects have equal measures Complementary and supplementary Add together two pieces to equal a known total (complementary = 90; supplementary = 180) Transformations Rotations (Positive rotations are CounterClockWise), Reflections, Translations Preimage and Image, Rigid and Non-rigid (Vocabulary); Find one from the other using a rule Infer a rule from Preimage and Image State whether a transformation is Rigid or Non-rigid Image of point or image of shape

Shapes Triangles Congruence CPCTC – Corresponding Parts of Congruent Triangles are Congruent Write a congruence statement Exterior angle and their relation to “remote interior angles” Medians and Altitudes (orthocenter, centroid, etc) Quadrilaterals Types of Quadrilaterals (Square, rectangle, rhombus, parallelogram, trapezoid) What angles or sides are congruent? What is parallel? Any relation with the diagonals? Congruent angles and sides Set up equations to solve. Supplementary Angles Set up equations to solve.

And some assorted others. Midsegment theorem Perpendicular bisectors Midpoint Bisector Two-Column Proofs Given (usually first or as needed) Prove (last) Definitions Postulates and Theorems Triangle Sum Theorem

Section 1

Section 2

Section 3 Transformations Rotations (Positive rotations are CounterClockWise), Reflections, Translations Rotations will be given relative to a point. This is the center around which all points revolve. Reflections are generally over the x-axis (“in the x-axis”), over the y-axis (“in the y-axis”), or over some other line. Imagine placing a mirror on that line, where the the IMAGE appear? Translations are slides: some amount along x and some amount along y. Preimage and Image, Rigid and Non-rigid (Vocabulary); Find one from the other using a rule (ex. (x,y)  (x – 1, y+22) slides every point one unit left and 22 units up). Recognize a rule from Preimage (object before transformation) and Image (object after transform) ex. preimage = (46, 30), image = (57, 22). The point translates 11 units left and 25 units up. (x,y)  (x +11, y - 8) State whether a transformation is Rigid or Non-rigid Rigid indicates that an object or DOES NOT CHANGE SIZE OR SHAPE. Image of point or image of shape

Section 4 Triangles Congruence CPCTC – Corresponding Parts of Congruent Triangles are Congruent Write a congruence statement Use the information in the diagram to prove that the two triangles which make up the shape are congruent. Reason Given Reflexive Property (congruent to itself) SSS

Exterior angle & their relation to “remote interior angles”

REASON By the Linear Pair Postulate Triangle Sum Theorem Substitution Subtraction Prop of Equality (POE) Commutative Property

Medians and centroid The median is a vocabulary term to describe a line segment that connects a vertex in a triangle to the midpoint of the opposite side. Since there are 3 vertices (plural of vertex) there are 3 medians that can be drawn. The Centroid is also called the “Center of Mass”, it is a special point where the object balances.

Altitudes and orthocenter

Incenter

Section 5 What shape(s) has(have) a pair of parallel sides that have different lengths? What shape(s) has(have) four congruent sides? What shape(s) has(have) four right internal angles?

Section 6 – More Quadrilaterals