Triangle eometry Isometric Triangles Lesson 1 Review of all the TORMS in OMTRY that you know or soon will know!. Triangles 1. The sum of the measures of the interior angles of a triangle is 180º (Triangle Sum Theorem) 2. n isosceles triangle has two congruent sides. 3. In an isosceles triangle, the angles opposite the congruent sides are congruent. 4. The axis of symmetry of an isosceles triangle is a median, a perpendicular bisector, an angle bisector & an altitude of the triangle. 5. n equilateral triangle has three congruent sides. 6. In an equilateral triangle, each angle measures 60º. 7. ll three axes of symmetry of an equilateral triangle are the medians, perpendicular bisectors, angle bisectors & altitudes of the triangle. 8. In a right triangle, the side opposite a 30º angle is one half the length of the hypotenuse. 9. In a right triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides. (Pythagorean Theorem) 10. In any right triangle, the acute angles are complementary. 11. In any isosceles right triangle, each of the acute angles measures 45º 12. In any triangle, the measure of an exterior angle is equal to the sum of the two opposite interior angles
Quadrilaterals 1. The sum of the measures of the interior angles of a quadrilateral is 360º. Squares 1. square has four congruent sides. 2. In a square, each angle measures 90º. 3. The diagonals of a square bisect each other perpendicularly. Rhombuses 1. rhombus has four congruent parts. 2. The diagonals of a rhombus are perpendicular to each other. Rectangles 1. The opposite sides of a rectangle are congruent. 2. In a rectangle, each angle measures 90º. 3. The diagonals of a rectangle bisect each other. Parallelograms 1. The opposite sides of a parallelogram are congruent. 2. The opposite angles of a parallelogram are congruent. 3. The consecutive angles of a parallelogram are supplementary. 4. The diagonals of a parallelogram bisect each other. Kites 1. kite has two pairs of congruent sides. 2. The diagonals of a kite are perpendicular to each other and one diagonal will be bisected. Isosceles Trapezoids 1. n isosceles trapezoid has one pair of congruent sides and two congruent angles. 2. trapezoid has only one pair of parallel sides. Polygons 1. The sum of the interior angles of a convex polygon is (n 2) x 180 o. 2. ach angle of a regular polygon is (n 2) x 180 o n ircles 1. In a circle, the measure of the radius is half the measure of the diameter. 2. ll the diameters of a circle are congruent. 3. ll the radii of a circle are congruent. Now for the new ones! ngles 1. Two adjacent angles are complementary when the sum of their measures is 90 o. 2. Two adjacent angles are supplementary when the sum of their measures is 180 o. 3. Vertically opposite angles are congruent. (VO) 4. orresponding angles formed by parallel lines and a transversal are congruent. (corr. angles are ) 5. lternate interior angles formed by parallel lines and a transversal are congruent. (alt. int. angles are ) 6. lternate exterior angles formed by parallel lines and a transversal are congruent. (alt. ext. angles are ) 7. If the corresponding angles are congruent, or the alternate interior angles are congruent, or the alternate exterior angles are congruent, then the two lines intersected by a transversal are parallel.
Lesson 1: Name that angle! 3 4 6 1 7 2 5 If there are more than 2 rays meeting at a vertex, then you must use three letters to name an angle 1 2 3 4 5 omplementary ngles add to 90 Supplementary ngles add to 180
Vertically Opposite ngles are congruent Parallel Lines Theorems corresponding angles formed by parallel lines and a transversal are congruent l 2 transversal is a line that intersects two or more lines (in the same plane) and l 2 are parallel
alternate interior angles formed by parallel lines and a transversal are congruent l 2 and l 2 are parallel alternate exterior angles formed by parallel lines and a transversal are congruent l 2 and l 2 are parallel
We have seen in the three previous cases that if the two lines are parallel and they are intersected by a transversal, then the corresponding (or alt. inter. or alt. ext) angles are ONRUNT... WLL!... We can also say that if the corresponding (or alt. inter. or alt. ext) angles created by a transversal are congruent...tn the lines must be PRLLL. xample: etermine the measures of angles 1, 2 and 3 1 2 3
xample: Solve for the variable x xample: Solve for x diagram is not necessarily to scale xample: Solve for x P
xample: K J statement justification I 1 2 3 4 5 6 7 8 9 10 11 12 xample: K J I The exterior angle of a triangle is equal to the sum of the the two, opposite interior angles x x+y y
xample: 35? 38 xample: 35? 38 omework: Page 190 #1 Page 191 #2,3,4 Page 192 #5,6,7,8,9 e sure to make / charts Page 193 #11