You MUST know the big 3 formulas!

Transcription

1 Name: Geometry Pd. Unit 3 Lines & Angles Review Midterm Review 3-1 Writing equations of lines. Determining slope and y intercept given an equation Writing the equation of a line given a graph. Graphing Linear Equation 3-2 Point Slope Form 3-3 Using slope and y intercept to determine if line are parallel, perpendicular, or the same line. Same slope Parallel Opposite reciprocal slope Perpendicular Same slope and y-intercept same line 3-4 Writing equations of lines. Parallel lines Same slope as original, use one point on the line then sub into Perpendicular lines opposite reciprocal slope of original, use point on the line then sub into 3-5 Slope of a line using slope formula Watch out for common mistakes! 1. Y s are on top! 2. Double negatives! Use your CALCULATOR! 3. Simplify fractions! 3-6 Distance and Midpoint Distance or length: You MUST know the big 3 formulas! Midpoint Formula: Watch out for common mistakes! 1. Take it slow, show all steps. 2. Don t forget parentheses and comma for Midpoint! 3-7 Writing equation of perpendicular Bisector. Find slope of given line, take the opposite reciprocal. Calculate Midpoint of given line. Sub the new slope and midpoint into make sure you sub in MIDPOINT. Not the points on line 3-8 QUIZ- Make sure you look at all your mistakes! Simplify Radicals make prime factor tree pairs go outside multiply by anything already outside. 3-9 Angles and notation Vertical angles Across from each other, always congruent Angles at a point Make a full circle add up to 360 degrees. Linear pairs Adjacent and supplementary add up to 180 degrees. Supplementary angles two angles that add up to 180 degrees. Complementary angles two angles that add up to 90 degrees Angles on a transversal Alt. Interior, Alt. Exterior, Corresponding angles are if the lines are. Same-side Int., Same side Ext. are supplementary if the lines are Justifying parallel lines When justifying parallel lines you need to include 1. Type of angle pair 2.Relationship 3. Conclusion 3-12 Construction of parallel lines ( with justification) -Construction works because we are copying an angle into the corresponding position on the new line.

2 Unit 4 Triangle Theorems and Rules Review Part 1: Triangle Theorems and Rules Name of relationship In words/ Symbols Diagrams/ Hints/ Techniques 1. Side angle relationship The longest side is across from the largest angle. The medium length side is across from the mediumsized angle. The shortest side is across from the smallest angle 1. Solve for ALL angles in the triangle. 2. Draw arrows! 2. Triangle inequality Theorem 3. Pythagorean Theorem to find a missing side. Pythagorean Inequality to Classify triangles 4.Isosceles triangle Theorem The sum of the lengths of the two smaller sides of a triangle is greater than the length of the largest side. To find a range of possible sides, add two given sides, subtract them. a) c 2 = a 2 + b 2 C is longest side ( hypotenuse-across from the right angle) b) If c 2 a 2 + b 2 it is acute If c 2 a 2 + b 2 it is obtuse If c 2 a 2 + b 2 it is right Remember, c 2 must be on the left of = The base angles of an isosceles triangle are equal in measure. The sides opposite the base angles in an isosceles triangle (called legs) are equal in length. Add up the two smaller sides and compare to the largest side. If the sum is greater, it s a triangle! 2,3,4 (2+3) > 4? yes! If you see a right angle, it s a right triangle! use Pythagorean Theorem to solve for a missing side. WATCH OUT! If asked does this make a triangle you must use Theorem # 2- NOT PYTHAGOREAN. ERROR ALERT: you must SQUARE (power of 2) a, b and c, DIFFERENT FROM Theorem #2 seen above Angles opposite are congruent! If you see expressions, make them equal to each other! 5. Exterior angle theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle IN + IN =OUT

3 Unit 4 Triangle Theorems and Rules Review Continued Part 2- Segment in a triangle and Angle Relationships Name of relationship In words/ Symbols Diagrams/ Hints/ Techniques 1. Exterior angles in a polygon. Exterior angles and formed by extending a side of the triangle. a). ONE Exterior a) where n is the # of sides b) Sum of Exterior b) Sum is AlWAYS 360 degrees( NO MATH NEEDED) 2. Interior angles in a polygon. a) ONE Interior a) The supplement of on Exterior anglethey are linear pairs!--> Exterior + Interior = 180 b) Number of times 180. ( n-2)180 b) Sum of interior 3. Segments in a triangle: Medians- Goes to the midpoint of the opposite side creating two equal segments Altitudes-Are perpendicular to the opposite side creating right angles Perpendicular bisectors- Goes to the midpoint of opposite side and is perpendicular to it. Angle bisectors- bisects the angle at the vertex it goes through making 2 congruent angles. ** In Isosceles and Equilateral triangles these segments coincide! 4. Points of concurrence. 2 or more: medians Centroid : Always inside the triangle. Cuts each median into a 2:1 ratio Altitudes Orthocenter: Inside for acute triangles, on the triangle for right triangles and outside for obtuse triangles. angle bisectors Incenter: Always inside the triangle. perpendicular bisectors Circumcenter: Inside for acute triangles, on the triangle for right triangles and outside for obtuse triangles. 5.Centroid and Ratios Centroid cuts every median into a 2:1 ratio. Use this ratio to set up equation 2x + 1x= whole length of median. Remember! One exterior and one interior angle add up to 180 degrees! ALL OF MY CHILDREN ARE BRING IN PEANUT BUTTER COOKIES. Read carefully- What is the segment they want? Sometimes you need to substitute back in! 6. Auxiliary Lines Use with non-traditional diagrams. Use with non-traditional diagrams. Extend lines to help you find: Linear pairs, special angle pair relationships, vertical angles, triangles.

4 Unit 3 Practice: 1. Write the equation of the perpendicular bisector of GH, given that G(2,-1) and H(10, -3). 2. Solve for x. 3. The midpoint of ABis M ( 4,2). If the coordinates of A are ( 6,-4), what are the coordinates of B? 4. State whether the lines represented by the equations and 4 2 x 2 perpendicular, neither, or the same line. Justify your answer. y are parallel, Unit 4: Triangles Questions 5. Solve for x

5 6. In the diagram below of DACE, medians AD, EB and CF intersect at G. The length of FG is 12 cm. What is the length, in centimeters, of GC? 7. Solve for the measure of g. 8. In the accompanying diagram, isosceles is congruent to isosceles. Find and

6 9. Use the diagram below to answer the following: a) Solve for and label in diagram the angles of SAT. State and determine the largest side of SAT. b) Solve for and label in diagram the angles of RSA. State and determine the smallest side of RSA. c) explain why RA ST 10. Given the rectangle at the right, with diagonal 19 inches and height 10 inches. Find the width of the rectangle to the nearest inch.