Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Penrose tiling wikipedia , lookup
Technical drawing wikipedia , lookup
Perceived visual angle wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
5-1 Classifying Triangles Today we will be learning how to classify triangles according to length of sides and measurement of the angles. First we will learn to classify by the ANGLES Right triangles have ONE right angle Acute Angle Acute Triangles have three acute angles Smaller than 90o Smaller than 90o Smaller than 90o Obtuse Angle Obtuse Triangles have ONE obtuse angle We will now learn to classify triangles by their sides. Equilateral Triangles have 3 equal sides If you collapsed all of the sides they would form a line. Isosceles Triangles have 2 equal sides. Scalene Triangles have NO equal sides. Classifying Triangles by Their Sides EQUILATERAL – 3 congruent sides ISOSCELES – at least two sides congruent EQUILATERAL ISOSCELES SCALENE – no sides congruent SCALENE Classifying Triangles by Their Angles EQUIANGULAR – all angles are congruent ACUTE – all angles are acute RIGHT – one right angle ACUTE EQUIANGULAR OBTUSE – one obtuse angle RIGHT OBTUSE Can You Classify the Different Triangles in the Picture Below? Triangle AED = Equilateral, Equiangular Triangle ABC = Equilateral, Equiangular Triangle ACD = Isosceles, Obtuse Triangle ACE = Scalene, Right Classify the following triangles: AED, ABC, ACD, ACE Slide 3 of 3 Slide 3 of 3 Slide 3 of 3 Slide 3 of 3 You have now learned that triangles can be classified by either their sides or their angles. 5-2 ANGLES OF A TRIANGLE Slide 1 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 Slide 2 of 2 EXAMPLE 3 Find an angle measure Find m JKM. SOLUTION STEP 1 Write and solve an equation to find the value of x. (2x – 5)° = 70° + x° x = 75 Apply the Exterior Angle Theorem. Solve for x. STEP 2 Substitute 75 for x in 2x – 5 to find m JKM. 2x – 5 = 2 75 – 5 = 145 ANSWER The measure of JKM is 145°. GUIDED PRACTICE for Examples 3 and 4 3. Find the measure of 1 in the diagram shown. ANSWER The measure of 1 in the diagram is 65°. GUIDED PRACTICE for Examples 3 and 4 4. Find the measure of each interior angle of ABC, where m A = x ° , m B = 2x° , and m C = 3x°. SOLUTION A+ B+ x C = 180° x + 2x + 3x = 180° 6x = 180° x = 30° B = 2x = 2(30) = 60° C = 3x = 3(30) = 90° 2x 3x GUIDED PRACTICE for Examples 3 and 4 5. Find the measures of the acute angles of the right triangle in the diagram shown. ANSWER 26° and 64°