Review for Final Equations of lines General Angle Relationships Parallel Lines and Transversals Construction Transformations Proofs

Equations of Lines Given two points writing the equation of a line Slope intercept Point Slope of a line 1. Find the slope 2. Calculate the y-int Substitute in the slope and one set of ordered pairs (x,y) you should them be able to solve for b 3. Write the equation of a line

Parallel and Perpendicular Lines Parallel Lines - slopes are the same need to calculate a new y-int Sub in same slope, sub in different x and y values and solve for new b Perpendicular lines - slopes are opposite reciprocals, which means flip the fraction and change the sign to the opposite of what the original equation was Perpendicular lines can have the same y-int, but you need to calculate it like all the other equations

Horizontal and Vertical Lines Zero slope is a slope when the rise of the line is zero Lines with a zero slope are horizontal y=number Undefined slope is a slope when the run is zero Lines with an undefined slope are vertical x=number

Examples Given the following ordered pairs find the equation of the line. (2, -5) and ( -4,7)

Example Given the following equation of the line find the following: (solve the equation for y to find the slope) Equation of a line parallel and through (-2,2) 2. Equation of a line perpendicular and through (3,-1)

Parallel

Perpendicular

Midpoint Know how to find the midpoint of a segment Know how to work backwards to find the other endpoint

Examples Given the following endpoints of a segment find the midpoint. A(5,1) and B(-3,-7)

Example Given the one endpoint of a segment A(2,4) and the midpoint of the segment B(-1,3) Find the other endpoint.

General Angles Know the relationships Vertical Angles Linear Pairs Supplementary (supplement) Complementary (complement) When do angles add to 360

Example

Example

Parallel Lines and Transversal If lines are parallel this is true Corresponding Angles - congruent 1 and 5 2 and 6 3 and 7 110 and 4 Alternate Interior Angles - congruent 3 and 5 2 and 4 Alternate Exterior Angles - congruent 1 and 7 110 and 6 Same Side Interior Angles – supplementary 3 and 4 2 and 5

Example How are 4x+28 and 5x+8 related, walk your way around to prove 4x+48 corresponds to 19 19 is Alternate Exterior angle to 5x+8 Makes angles congruent Find all missing angles and explain why you know that angle in relation to other angles

Example

Constructions Know cheat sheet – what are the main constructions and what ideas deal with what type Altitude is perpendicular line from vertex to side opposite Median is a segment from vertex to midpoint of opposite side, need to construct perpendicular bisector to find midpoint Perpendicular Bisector constructs a line that is equidistant from the endpoints of the segment Angle Bisector constructs a ray that is equidistant from the sides of the angle

Example Draw a triangle and construct the altitude from one vertex and the median from the other

Example Mark 2 points on your paper. Find a path that is equidistant from both point no matter where on the path you are This would be the perpendicular bisector because it is equidistant from the two points

Transformations Know basic ideas of transformation Know transformation rules Do the given transformation Identify the transformation

Transformations Translation – slide left, right up or down, add or subtract to the x or y coordinate (x+num, y+num) Reflect – mirror image over a line over x-axis (x,-y) over y-axis (-x,y) over line y=x (y,x) Rotate around the origin 180 (-x,-y) Some of the transformations can be doubles of other know how to combine them.

Example Part A: On your grid, draw the triangle J’K’L’, the image of triangle JKL after it has been reflected over the y-axis. Be sure to label your vertices   Part B: On your grid, draw the triangle J’’K’’L’’, the image of J’K’L’ after it has been reflected over the line y=x. Be sure to label your vertices

Example Write the rule for the given transformation. (x,y)- ( ___, ___), show some work on how you came to that conclusion. (5,-7) Original New

Proofs Know set up of two column proof 1st Givens 2nd Prove other parts congruent need at least 3 3rd State triangles congruent 4th CPCTC of other parts of triangle

Proofs Know cheat sheet and key terms Visual – Vertical angles and Reflexive sides Given information used for reasons Midpoint Angle Bisector Segment Bisector Perpendicular Segment is a perpendicular Bisector Parallel sides

Example Given: BD is a bisector of < ABC DB is perpendicular to AC Prove: BD bisects AC

Example Are the triangles congruent, give conjecture if they are give reason if they are not.