* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Answer
Survey
Document related concepts
History of geometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Penrose tiling wikipedia , lookup
Golden ratio wikipedia , lookup
Technical drawing wikipedia , lookup
Apollonian network wikipedia , lookup
Multilateration wikipedia , lookup
Euler angles wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Incircle and excircles of a triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
Transcript
Lesson 4-1 Classifying Triangles Transparency 4-1 5-Minute Check on Chapter 3 Refer to the figure. 1. What is the special name given to the pair of angles shown by 2 and 6? 2. Find m3. 3. Find m4. 4. Find the slope of the line that contains the points at (4, 4) and (2, –5). 5. Write the equation of a line in slope-intercept form that has a slope of ¾ and contains the point at (0, 5). 6. Standardized Test Practice: What is the slope of a line that is perpendicular to the line y = 2/3x – 5? A –3/2 B –2/3 C 2/3 D 3/2 Transparency 4-1 5-Minute Check on Chapter 3 Refer to the figure. 1. What is the special name given to the pair of angles shown by 2 and 6? corresponding angles 2. Find m3. 62 3. Find m4. 118 4. Find the slope of the line that contains the points at (4, 4) and (2, –5). 9/2 5. Write the equation of a line in slope-intercept form that has a slope of ¾ and contains the point at (0, 5). y = 3/4x + 5 6. Standardized Test Practice: What is the slope of a line that is perpendicular to the line y = 2/3x – 5? A –3/2 B –2/3 C 2/3 D 3/2 Objectives • Identify and classify triangles by angles • Identify and classify triangles by sides Vocabulary • Scalene – no sides are congruent • Isosceles – two sides are congruent • Equilateral – all sides are congruent • Equiangular – all angles are congruent … By angles Acute triangle All angles < 90 Classifying Triangles Obtuse triangle One angle > 90 Right triangle One angle = 90 … By sides Scalene triangle No sides are Isosceles triangle Equilateral triangle Two sides are All sides are Classify by angle measure Classifying Triangles Classify by number of congruent sides Angles Measure of one angle is 90° Measure of one angle > 90° Measure of all angles < 90° 3 congruent angles Sides Right Scalene No sides congruent Isosceles 2 sides congruent Equilateral 3 sides congruent Obtuse Acute Equiangular ARCHITECTURE The triangular truss below is modeled for steel construction. Classify JMN, JKO, and OLN as acute, equiangular, obtuse, or right. Answer: JMN has one angle with measure greater than 90, so it is an obtuse triangle. JKO has one angle with measure equal to 90, so it is a right triangle. OLN is an acute triangle with all angles congruent, so it is an equiangular triangle. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ABC, ACD, and ADE as acute, equiangular, obtuse, or right. Answer: ABC is acute. ACD is obtuse. ADE is right. Identify the indicated triangles in the figure if Isosceles triangles Isosceles triangles have at least two sides congruent. Answer: UTX and UVX are isosceles. Scalene triangles Scalene triangles have no congruent sides. Answer: VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene. Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, EBC, DEB, DCE, ADC, ABD ALGEBRA Find d and the measure of each side of equilateral triangle KLM if KL = d + 2, LM = 12 – d and KM = 4d – 13. Since KLM is equilateral, each side has the same length. So KL = KM. Substitution Subtract d from each side. Add 13 to each side. Divide each side by 3. Next, substitute to find the length of each side. Answer: For KLM, and the measure of each side is 7. ALGEBRA Find d and the measure of each side of equilateral triangle if and Answer: COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides. Use the distance formula to find the lengths of each side. Answer: ; since all 3 sides have different lengths, RST is scalene. Find the measures of the sides of ABC. Classify the triangle by sides. Answer: ; since all 3 sides have different lengths, ABC is scalene. Summary & Homework • Summary: – Triangles can be classified by their angles as acute, obtuse or right – Triangles can be classified by their sides as scalene, isosceles or equilateral • Homework: – pg 180-1: 5, 9, 13-18, 27