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
Line (geometry) wikipedia , lookup
Golden ratio wikipedia , lookup
Perceived visual angle wikipedia , lookup
Multilateration wikipedia , lookup
History of trigonometry wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euler angles wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Homework Solutions – Section 4.2: pg.178: 1, 3*, 5, 7, 8*, 13-15 1. Given: An isosceles triangle and the median to its base Prove: The median is the perpendicular bisector to the base. B Given: Prove: A D C 3. On problem set 5. The altitude to a side of a scalene triangle forms two congruent angles with that side of the triangle. B D Given: Prove: A Statements 1. 2. 3. 4. Reasons 1. Given 2. An altitude is perpendicular to the side of a triangle. 3. If two lines are perpendicular, then they form right angles. 4. If two angles are right then they are congruent. C 7. If the base of an isosceles triangle is extended in both directions, then the exterior angles formed are congruent. C Given: Prove: A Statements 1. 2. 3. 4. 5. 13. B E D Reasons 1. Given 2. if a triangle is isos, then it has two congruent sides. 3. If two sides of a triangle are congruent then the angles opposite those sides are also congruent. 4. If two angles form a straight angle then they are supplementary. 5. If two angles are supplementary to congruent angles then they are congruent. If each pair of opposite sides of a four-sided figure are congruent, then the segments joining opposite vertices bisect each other. Given: A D Prove: E B C 14. If a point on the base of an isosceles triangle is equidistant from the midpoints of the legs, then that point is the midpoint of the base. (equidistant means that if segments were drawn in then they would be congruent). C Given: Prove: B A 15. D E F If a point in the interior of an angle (between the sides) is equidistant from the sides of the angle, then the ray joining the vertex of the angle to this point bisects the angle. (Hint: the distance from a point to a line is defined as the length of the perpendicular segment from the point to the line). C Given: ⃗⃗⃗⃗⃗ , ⃗⃗⃗⃗⃗ B Prove: ⃗⃗⃗⃗⃗ D F A G E