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
Multilateration wikipedia , lookup
Noether's theorem wikipedia , lookup
Euler angles wikipedia , lookup
Integer triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Perceived visual angle wikipedia , lookup
Name: _____________________________ Geometry Date: ____________ Do – Now: Find the value of x *************************************************************************************** Exterior Angle Theorem and Angle-Side Relationships Exterior Angle Theorem and An Inequality Involving the Exterior Angle Theorem The exterior angle theorem states that ____________________ Therefore, the measure of an exterior angle must be greater than the measure of either nonadjacent interior angles. Ex: Examples: #1 and 2, use diagram to the right. 1) Name all angles whose measures must be less than m<7. 2) Name all angles whose measures must be greater than m<6. 3) Solve for x. 4) Solve for x. Angle Side Relationships in Triangles: Theorem Picture If one side of a triangle is longer than another side, than the angle opposite the longer side is greater in measure than the angle opposite the shorter side. If one angle of a triangle is greater in measure than another angle, then the side opposite the larger angle is longer than the sure opposite the smaller angle. Examples: 1) List the angles in order from shortest to longest. 2) List the sides in order from shortest to longest. a) 3) Which is the longest side of b) ? Explanation Name: ______________________ Homework: Exterior Angle Theorem and Angle-Side Relationships in Triangles 1) Solve for x and j. 2) In the diagram below of . What is 3) In the diagram below of , side is extended to point D, , , and ? , side is extended to point A. Which statement must be true? 1) 2) 3) 4) 4) In scalene triangle ABC, longest to shortest? 1) , , 2) , , 3) , , 4) , , and . What is the order of the sides in length, from 5) As shown in the diagram below, , and is a diagonal of trapezoid STAR, . Determine and state the longest side of , . Some Review… 6) Solve for g. 7) Solve for h. ,