“Honors Euclidean Geometry” – UNIT I: Logic and Reasoning, Points/Lines/Planes/Angles

“Geometry” published by HOLT, RINEHART, & WINSTON

Target Time: 13-17 days

ESSENTIAL STANDARD / ESSENTIAL QUESTION / DEPTH for MASTERY / Sections / COMMENTS
#2—Uses algebraic skills and concepts to solve geometric problems throughout geometry / What algebra skills and concepts are utilized in geometry? / All / Throughout unit / Stress algebra
#5—Recognizes valid deductive reasoning; constructs and uses if-then, converse, inverse, and contrapositive statements. / What are the different forms of a conditional statement? / All / 2.2
12.3
#8—Identifies, describes, and contrasts points, lines, planes, segments, and rays / What are the characteristics of points, lines, planes, segments, and rays? / All / 1.1
#9—Identifies, defines, estimates, and measures segments and angles (acute, obtuse, right, straight, complementary, supplementary, adjacent, vertical, congruent, and linear pair) / How are segments and angles measured and classified? / All / 1.2
1.3
#10—Identifies and defines or describes properties associated with points (distance, between, collinear, coplanar), segments (midpoint, congruence, interior, exterior), and lines and planes (perpendicular, parallel, intersecting) / What properties are associated with points, segments, angles, lines, and planes? / All / 1.1
1.2
1.3
1.4
#12—Recognizes parallel lines and planes, skew lines, and pairs of angles formed when two lines are cut by a transversal (alternate and same side, interior and exterior, corresponding) / How are lines, planes, and angles related? / All / 3.3
(skew p380) / Parallel and Perpendicular Postulates
#45—Applies the distance and midpoint formulas / How are the distance and midpoint formulas used? / All / 5.6
IMPORTANT STANDARD / ESSENTIAL QUESTION / DEPTH for MASTERY / Sections / COMMENTS
#1—Solves problems and practical applications using appropriate approaches and tools (including calculators and computers) and judges the reasonableness of results / How do we solve problems and practical applications and judge the reasonableness of the results? / All / Throughout unit
#4—Uses inductive and deductive reasoning to reach conclusions, identifies conjectures and counterexamples, and describes the nature of a deductive mathematical system / What is the difference between inductive and deductive reasoning? / All / 2.1
2.2
2.5
#6—Uses formal and/or informal logical reasoning processes / How do you use formal and informal reasoning processes? / All / 2.1
2.2
2.5
#7—Uses inductive and deductive reasoning to prove conjectures in written form such as paragraph, two-column, or flow chart / How do your prove theorems and how do you demonstrate conjectures? / All / 2.4
2.5 / Deemphasize formal proof and emphasize logic
#13—Applies basic facts about points, lines, and planes, and about perpendicular and parallel lines and planes. / How are points, lines and planes related? / All / 1.1
1.2
1.4
3.3
3.8
COMPACT STANDARD / ESSENTIAL QUESTION / DEPTH for MASTERY / Sections / COMMENTS
#3—Uses visualization skills to explore and interpret both two- and three- dimensional geometric figures using such topics as projections, cross sections, and locus problems / How can visualization skills help you explore both solid and plane geometry? / Lines, points, planes, two- and three- dimensional / 1.1
#16—Uses tools such as compass and straightedge, paper folding, tracing paper, mira, or computer to construct congruent segments, angles, triangles, and circles; an angle bisector; a perpendicular bisector; a perpendicular line from a point on a line; parallel lines; proportional segments; tangents; and inscribed and circumscribed polygons / What are the basic tools and construction methods used in geometry? / OMIT proportional segments; tangents; and inscribed and circumscribed polygons / Throughout unit
#44—Identifies and graphs ordered pairs of numbers in the coordinate plane / How do we graph and/or identify ordered pairs in a coordinate plane? / All / Supplement
#46—Finds the slope of a line, writes an equation of a line, and graphs equations of lines / How do we find the slope, equation, and graph of a line? / All / Supplement
#47—Finds the coordinates of the point of intersection of two lines, using algebra, graphing, and appropriate technology / How do you find the coordinates of the point of intersection of two lines in the coordinate plane? / All / Supplement

EOCT Domains Taught in this Unit: Logic and Reasoning; Points, Lines, Planes, and Angles; Coordinate Geometry