Geometry Course Summary Department: Math. Semester 1

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1 Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give the appropriate notation for line, segment, ray, and angle. Draw representations of given geometric situations Determine whether points are collinear or coplanar Determine the distance or length of any segment given the coordinates of its endpoints Use the segment addition postulate to determine the length of segments that are separated into two or more segments Classify angles into groups according to the measure of their angles Use angle addition postulate to determine the measure of angles that are separated into two or more angles Use the midpoint formula to find the midpoint between two given endpoints Find one endpoint given the other endpoint and the midpoint Tell the difference between intersect and bisect Identify vertical angles and linear pairs. Find missing measurements using the fact that vertical angles are equal and linear pairs = 180 Find missing measures using the ideas of complementary and supplementary Find perimeter of any basic figure Use area formulas for triangle, rectangle, square, and circle Find a missing measurement given the area Learning Objective #2 Geometric Thinking Targets to Meet Learning Objective #2 Write conditional statements in if-then form Label parts of conditional statement Write converse, inverse, and contrapositive Write biconditional statements if the properties for a biconditional statement exist Use law of detachment and syllogism to make conjectures from other statements Use inductive and deductive reasoning to make conjectures about given information Use the algebraic properties of equality to solve equations and give a proof Write a two-column proof for segment theorems Write a two-column proof for angle theorems 7 blocks

2 Learning Objective #3 Parallel and Perpendicular Lines Targets to Meet Learning Objective #3 Parallel lines, parallel planes, skew lines, and perpendicular lines Identify special angles formed by a transversal Use angle relationship postulates to solve for missing measurements in pictures of parallel lines cut by a transversal. Prove that two angles are either congruent or supplementary using angle relationship postulates Prove that two lines are parallel by using angle relationship postulates Identify properties that exist when multiple lines are parallel or perpendicular and use those properties to design a city of their own. Write the equation of a line given a variety of information Write the equation of a line that is parallel to another and goes through a given point Write the equation of a line that is perpendicular to another and goes through a given point Learning Objective #4 Triangle Congruence Targets to Meet Learning Objective #4 Classify triangles according to the angle measures and side lengths. Define basic parts of triangles Find the third angle in a triangle Use the exterior angle theorem to find missing measurements Recognize congruent triangles by identifying corresponding parts Use congruence of figures to find missing measurements Use given information to recognize which congruence postulate could be used to prove that two triangles are congruent Use congruence postulates to write two column proofs for congruent triangles Understand that proving two triangles are congruent can also lead to proving that other corresponding pieces must also be congruent (CPCTC) Know the parts of an isosceles triangle Understand the relationship between base angles and legs in an isosceles triangle Use the hypotenuse-leg congruence theorem to write a two column proof for congruent triangles

3 Learning Objective #5 Special Triangle Segments and Transformations Semester 2 Targets to Meet Learning Objective #5 Use the properties of perpendicular bisectors and angle bisectors in a triangle Identify medians and altitudes of a triangle Use the midsegment of a triangle to solve for missing lengths Use triangle inequalities to describe properties of the third side of a triangle. Describe rigid transformations in a coordinate plane as a translation, reflection, or rotation Identify, use, and algebraically describe reflections in the coordinate plane Students will be able to identify, use, and algebraically describe translations and rotations in the coordinate plane Learning Objective #6 Quadrilaterals Targets to Meet Learning Objective #6 Classify polygons according to number of sides and special properties Use the sum of quadrilaterals to find missing angle measurements in a quadrilateral Use special properties of parallelograms to find missing measurements in a parallelogram. Prove that a quadrilateral is a parallelogram by identifying special properties of a parallelogram Find values within a quadrilateral that would make the figure be a parallelogram Use properties of special parallelograms to find missing measurements in a figure. Compare and contrast different types of parallelograms Use properties of trapezoids and kites to find missing measurements. Use area formulas for quadrilaterals 7 blocks

4 Learning Objective #7 Similarity Targets to Meet Learning Objective #7 Student should be able to reduce ratios of the same unit or different units Student should be able to solve proportions Given a true proportion, students should be able to analyze new proportions and verify their validity Student should be able to determine whether two figures meet the properties of similarity Student should be able to find missing measurements in two similar figures using proportions Students should be able to determine whether two figures are similar by any of the three similarity postulates ( AA similarity, SSS Similarity, SAS Similarity) 6 blocks Learning Objective #8 Trigonometry and the Unit Circle Targets to Meet Learning Objective #8 Use the Pythagorean theorem to find missing pieces in a right triangle Use the Pythagorean theorem to help classify a triangle Discuss angle measures in terms of degrees or radians Convert between radians/degrees Fill in the unit circle for angle measures in both degrees and radians Find missing lengths in a triangle Find the missing lengths in a triangle. Use the and relationships to fill in the points on the unit circle Set up all trigonometric ratios for a right triangle Use a calculator to find trigonometric values for angles measured in degrees Use trigonometric ratios to find missing side lengths of a right triangle Use trigonometric ratios to find missing angle measures of a right triangle

5 Learning Objective #9 Circles Targets to Meet Learning Objective #9 Identify segments and lines related to circles. Use the arc addition postulate to find missing arc mesurments Use properties involving congruent chord/arcs to find missing measurements Use inscribed angles of any kind to find missing arc measures Write the equation of a circle given the radius and center Graph a circle from the equation Learning Objective #10 Polygons and Sectors Targets to Meet Learning Objective #10 Find the surface area of a prism, cylinder, pyramid, or cone Find the volume of prisms, cylinders, pyramids, and cones Find the surface area and volume of a sphere Find and use the scale factor of similar solids 5 blocks Learning Objective #11 3 Dimensional Figures Targets to Meet Learning Objective #11 Find the surface area of a prism, cylinder, pyramid, or cone Find the volume of prisms, cylinders, pyramids, and cones Find the surface area and volume of a sphere Find and use the scale factor of similar solids