SOL G.2 The student will use the relationships between angles formed by two cut by a transversal to a) determine whether two lines are parallel; b) verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and c) solve real-world problems involving angles formed when parallel lines are cut by a transversal. HINTS AND NOTES To prove that 2 lines are parallel, you must be able to prove: -corresponding angles are congruent OR -alternate interior angles are congruent OR -alternate exterior angles are congruent OR -consecutive interior angles are supplementary OR -both lines are perpendicular to the same line OR -both lines are parallel to the same line OR -the two lines have the same slope. Slope = Parallel – have the same identical slope Perpendicular – have negative reciprocal slopes PRACTICE G.2 Using the information in the diagram, which is true? A B C D Line a is parallel to line b if A B C D What value for x will show that lines l and m are parallel?
Translation – slides over Rotation – turns around a point Dilation – shrinks or blows up A line of symmetry is a line that can cut an object so that if it is folded all sides and angles will match perfectly. D Consider the figure provided. Which of the following is a rotation in the plane of the given figure? A B C D The polygon A’B’C’D’E’ is - ? A a translation of ABCDE across the x-axis B a clockwise rotation of ABCDE about the origin C a reflection of ABCDE across the y-axis D a reflection of ABCDE across the x-axis Which point is the greatest distance from the origin? A B C D Which polygon shown below has only one line of symmetry? A
Click and Drag. These questions give you the choices for your answer or answers. You must click on each correct answer and drag it to the appropriate box. You must get all of them correct to get the answer correct. For our purposes, just write the correct answers in the boxes. Determine the reason to justify each statement. You may choose from the Definitions, Theorems, and Postulates listed in the 2-column table. Given AAS Transitive Property of Congruence SAS Reflexive Property of Congruence ASA Symmetric Property of Congruence SSA If 2 sides of a triangle are congruent, then the angles opposite them are congruent Substitution Property of Equality Definition of Bisector Definition of Congruency Definition of Isosceles Triangle Reflexive Property of Equality A Kite has 2 congruent sides Symmetric Property of Equality bisects . is isosceles with base . Prove: Statements Reasons 1. bisects . 1. Given 2. 2. 3. 3. 4. 4. 5. 5. Determine if the pair of triangles is similar. If similar, highlight the similarity theorem to the box next to the triangle pairs. If not, then highlight “Not Similar”. Not Similar AA Similarity SAS Similarity SSS Similarity Not Similar AA Similarity SAS Similarity SSS Similarity Not Similar AA Similarity SAS Similarity SSS Similarity Not Similar AA Similarity SAS Similarity SSS Similarity
Figures SOL G.9 The student will verify characteristics of quadrilaterals and use properties of quadrilaterals to real-world problems. HINTS and NOTES Quadrilateral – polygon with four sides Properties: Parallelogram: Opposite sides Opposite sides parallel Opposite angles Consecutive angles are supplementary Diagonals bisect each Rectangle: Opposite sides Opposite sides parallel Opposite angles Consecutive angles are supplementary Diagonals bisect each Four angles (90o) PRACTICE G.9 The design for a quilt piece is made up of 6 congruent parallelograms. What is the measure of ? A B C D Figure ABCD is a rectangle. and are diagonals. AC = 30 meters and BC = 18 meters. What is the length of ? Dimensional