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- cours magistral - matière potentielle : notes
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WALCH EDUCATION Daily WarmUps GEOMETRY Texas Essential Knowledge and Skills
Jillian Gregory
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .v About the CDROM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vi Part 1: Geometric Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part 2: Geometric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Part 3: Dimensionality and the Geometry of Location . . . . . . . . . . . . . . 38 Part 4: Congruence and the Geometry of Size . . . . . . . . . . . . . . . . . . . . . 51 Part 5: Similarity and the Geometry of Shape . . . . . . . . . . . . . . . . . . . . . 85 Answer Key. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Daily Warm-Ups: Geometry, Texas Essential Knowledge and Skills
iii
Introduction The rst few minutes of each class period are critical, as they set the tone for the entire lesson. Set your class on the right path with these warmup problems, prompts, and brain benders. You can avoid wasted time by engaging your students from the minute they step into the classr The warmups are organized into ve parts based on the Geometry standards and expectations from the Texas Essential Knowledge and Skills for high school mathematics. The standards for Geometry include the following: • Geometric Structure • Geometric Patterns • Dimensionality and the Geometry of Location • Congruence and the Geometry of Size • Similarity and the Geometry of Shape Each warm-up can be classified under more than one standard and several expectations within each standard. For ease of use, the warmups have been categorized under the standard that best represents the goal of the problem. As a teacher, you can pick and choose the warmups you need each day based on your lesson plan.* Therefore, the order in which you use the problems is at your discretion. These warmups are a springboard to an engaging learning environment that will guarantee future success for your students. * You may select warmups based on particular standards using the Standards Correlations document on the accompanying CD.
Daily Warm-Ups: Geometry, Texas Essential Knowledge and Skills
v
Part 1: Geometric Structure
Overview Geometric Relationships • Use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships.
Logical Reasoning •Determine the validity of a conditional statement, its converse, inverse, and contrapositive. • Construct and justify statements about geometric figures and their properties. • Use deductive reasoning to prove a statement.
Classifying Triangles by Sides
1.
scalene triangle
isosceles triangle
equilateral triangle
no congruent sides
at least two congruent sides
three congruent sides
Classify each triangle below by its sides. a. b. 1.5 ft 7 cm 7 cm
7 cm
2.5 ft
1.5 ft
c. InABC,AB= 10 meters, BC= 14 meters, andCA= 22 meters.
2. Construct a scalene triangle and label the length of each side.
Daily Warm-Ups: Geometry, Texas Essential Knowledge and Skills
1
Isosceles Triangles: Median and Altitude The median of a triangle is a straight line from the vertex of the triangle to the midpoint of the opposite side. The altitude is the perpendicular distance from the vertex of a gure to the side opposite the vertex. The median and altitude of an isosceles triangle are shown below in the two gures.
2
median (dotted line)
altitude (solid line)
median
altitude
Draw the median and altitude for each isosceles triangle below.
1.
2.
3.
Daily Warm-Ups: Geometry, Texas Essential Knowledge and Skills
Equilateral and Equiangular 60˚ Anequilateral trianglehas three congruent sides and three congruent angles. 10 cm 10 cm An equilateral triangle is alsoequiangular.This means that if all three sides of a triangle are congruent, then all three angles of the triangle must be 60˚ 60˚ congruent, too. 10 cm On the other hand, an equiangular triangle is also equilateral. This means that if all three angles of a triangle are congruent, then all three sides of the triangle must be congruent as well.
Use a protractor and ruler to construct an equilateral triangle with side lengths of 3 inches. Label the side lengths and angles of the triangle.
Daily Warm-Ups: Geometry, Texas Essential Knowledge and Skills
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Conditional Statements A conditional statement is in the form “IfP,thenQ” and is classied as true or false as a whole. For instance, here is an example of a true conditional statement: If an angle measures 90°, then it is a right angle. This is true because all 90° angles are right angles, and all right angles measure 90°. Here is an example of a false conditional statement: If a polygon has four sides, then it is a rectangle. This is false because a polygon with four sides may or may not be a rectangle. It could be a square, a quadrilateral, or a trapezoid. 1. Classify each conditional statement below as true or false. a. If a triangle has three congruent sides, then it is an equilateral triangle.
4
b. If a quadrilateral has parallel sides, then it is a square.
2. Write a conditional statement about right triangles.
Daily Warm-Ups: Geometry, Texas Essential Knowledge and Skills
Answer Key
Part 1: Geometric Structure 1. 1. a. equilateral triangle or isosceles triangle b. isosceles triangle c. scalene triangle 2. Answers will vary. Verify that none of the side lengths are congruent and the triangle is not a right triangle. 1. median (dotted line)
2.
altitude inside (solid line)
altitude outside (dotted line)
median
altitude outside (dotted line)
altitude inside (solid line) Daily Warm-Ups: Geometry, Texas Esse
ti
3.
4.
3.
median
altitude inside (solid line)
3 in
60˚
3 in
altitude outside (dotted line)
101
60˚ 60˚ 3 in 1. a. True; an equilateral triangle does have three congruent sides. b. False; a quadrilateral with parallel sides can also be a rectangle or a parallelogram. 2. Answers will vary. Sample answer: If a triangle has a right angle, then it is a right triangle.
edge and Skills
