Solve the equations 8x - 4 = 3x - 39 5 (x - 9) = 2x + 15 Tuesday 04/23 Warm Up Solve the equations 8x - 4 = 3x - 39 5 (x - 9) = 2x + 15 4x - 10 = x + 3x - 2x

What is a “systems” of equations? Two (or more) linear equations What is the solution to a system of equations? The ordered pair (x, y) at which the lines intersect

What is it? Steps to Solve Substitution Method What is it? A method for solving systems of equations by substituting equations within each other Steps to Solve Step 1 : Solve one equation for x or y Step 3: Substitute your answer into the revised equation from Step 1 and solve for the other variable Step 2: Substitute this expression into the other equation and solve for the variable

Example 1: y = 6x 2x + 3y = -20 2x - 3y = -11 2x + y = 9 Example 2:

You Try! y = x + 9 3x + 8y = -5 2x + y = -2 5x + 3y = -8 You Try!

What is it? Steps to Solve Elimination Method A method of solving systems by adding or subtracting equations to eliminate a variable Steps to Solve Step 1: Make sure equations are lined up! Step 3: Solve the equation for the remaining variable. Step 2: Add or subtract equations to eliminate the variable with common coefficients Step 4: Substitute your answer into either original equation and solve for the other variable.

Example 1: x + 4y = 13 x - y = 3 x + 3y = 6 2x - 7y = -1 Example 2:

You Try! 3x - 10y = 14 3x - 9y = 15 9x + 3y = 12 2x + y = 5 You Try!

Wednesday 04/24 Warm Up System A: Choose your method Substitution or Elimination 8x + 5y = -13 3x + 4y = 10 System B: Choose your method Substitution or Elimination 4x - 3y = 18 2x + y = 4

Lines that never touch and are always the same distance apart Vocabulary Parallel Lines Lines that never touch and are always the same distance apart

A line that intersects more than one line Vocabulary Transversal A line that intersects more than one line

Angles whose sum is 180 degrees Vocabulary Supplementary Angles Angles whose sum is 180 degrees

Angles whose sum is 90 degrees Vocabulary Complementary Angles Angles whose sum is 90 degrees

Vocabulary Congruent Same size and shape. Fancy word for equal (Equal angles, side lengths, etc)

Parallel Lines and Transversals Name the parallel lines Name the transversal

Vertical Angles are congruent Vertical Angles Name and highlight the pairs vertical angles <1 and <4 <2 and <3 <5 and <8 <6 and <7

Corresponding angles are congruent Congruent Angles Corresponding angles are congruent Name and highlight the corresponding angles. <1 and <5 <2 and <6 <3 and <7 <4 and <8 Hint: Which ones match up in the same location?

Alternate Interior Angles Alternate Interior are congruent Name and highlight the alternate interior angles <3 and <6 <4 and <5 Hint: Alternate means opposite side of the transversal. Interior means inside of the parallel lines.

Alternate Exterior Angles Alternate exterior are congruent Name and highlight the alternate exterior angles <1 and <8 <2 and <7 Hint: alternate means opposite sides of the transversal. Exterior means outside,

Same side Interior Angles Same side interior angles are supplementary Name and highlight the same side interior angles <3 and <5 <4 and <6 Hint: Same side means on the same side of the transversal. Interior means inside.

Same side Exterior Angles Same side exterior angles are supplementary Name and highlight the alternate exterior angles <1 and <7 <2 and <8 Hint: Same side of transversal. Exterior means outside.

Given m∠1 is 120 degrees. Find the measure of all other angles. Example Given m∠1 is 120 degrees. Find the measure of all other angles.

Get out your assignment sheet to be signed! Thursday 04/25 Warm Up Get out your assignment sheet to be signed! Given the following, solve for x.

Dilations Discovery Activity

Dilations Dilation is a transformation in which a polygon is enlarged or reduced by a given factor around a given center point.

k represents the scale factor and how the polygon will grow. Dilations k represents the scale factor and how the polygon will grow. If k > 1, the polygon will grow If 0 < k < 1, the polygon will shrink If k = 1, the polygon will stay the same

To find the dilated coordinates... Multiply the x and y value by k! Example: Dilate the figure by a scale factor of k = 2. Will it grow, shrink or stay the same?

Simplify the following using exponent properties Friday 04/26 Warm Up Simplify the following using exponent properties

Solve the following proportions Monday 04/29 Warm Up Solve the following proportions

Motivational Monday

Similar Triangle Doodle Notes

Open your booklets to page 20 Complete #1-6 Tuesday 04/30 Warm Up Open your booklets to page 20 Complete #1-6

Check Worksheet Homework

Finish Similar Triangle Doodle Notes

Triangle Midsegment A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle. What is a midpoint?

Triangle Midsegment In a triangle, the segment joining the midpoints of any two sides of a triangles will be parallel to the third side and half its length OR

Example Answer: CD = 8

Example Answer: AC = 8

You Try! Answer: KI = 10

You Try! Answer: KJ = 9

Example Answer: X = -9

Example Answer: X = 5

You Try! Answer: X = 12

You Try! Answer: X = 12

Triangle Midsegment Theorem Folding Activity Cut out a triangle (any size!) and label the vertices (corners) as A, B, and C Fold A to C (don’t crease!) and pinch/label the midpoint as L. Fold B to C (don’t crease!) and pinch/label the midpoint as N. Fold C to the bottom of the triangle and draw in the line to connect L and N. Fold in B to C and A to C to create a rectangle. How does LN compare to AB?

Homework: pg. 21 #18 - 21

Open your booklets to page 31 Complete #1 - 6 Thursday 05/02 Warm Up We are in May!!!!!!!! Open your booklets to page 31 Complete #1 - 6

Check Homework: pg. 21 #18 - 21

Isosceles Triangle Theorem Guided Notes

Homework: Worksheet

Open your booklets to page 33 Complete #10 - 14 Friday 05/03 Warm Up Open your booklets to page 33 Complete #10 - 14

Check Homework Worksheet

Complete page 10 in your workbook! Monday 05/06 Warm Up Complete page 10 in your workbook!

Motivational Monday

Used to find missing side of a right triangle hypotenuse Pythagorean Theorem Used to find missing side of a right triangle hypotenuse c For any right triangle: a2 + b2 = c2 a legs b

Examples

Trigonometry: The study of triangle measurement

Trigonometric Ratios Sine: The ratio of the leg opposite the angle to the angle to the hypotenuse Cosine: The ratio of the leg adjacent the angle to the angle to the hypotenuse Tangent: The ratio of the leg opposite the angle to the leg adjacent to the angle

SOH - CAH - TOA SOH CAH TOA Some Old Hippie Caught Another Hippie REMEMBER!!! SOH CAH TOA Some Old Hippie Caught Another Hippie Trippin On Asphalt SOH - CAH - TOA Sin = opp/hyp Tan = opp/adj Cos = adj/hyp

Give each trig ratio as a fraction in simplest form

Homework page 52-53

Tuesday 05/07 Warm Up

Check Homework page 53

Finding Side Lengths Using Trig Note: Make sure your calculator is in degree mode

Your Turn!

Homework page 59 - 61

Wednesday 05/08 Warm Up

Check homework page 61

AGAIN! Make sure your calculator is in degree mode! Inverse SOH CAH TOA If you know the sin, cosine or tangent ratio of an angle, you can use the inverse of the ratio (sin-1, cos-1, tan-1) to find the measure of the angle. AGAIN! Make sure your calculator is in degree mode!

Finding Angle Measures

Your Turn!

Homework page 71 - 73

Thursday 05/09 Warm Up

Check homework page 72 - 73

Applications Angle of Elevation When looking UP to an object, the angle of elevation is formed by an observer’s line of sight and a horizontal line. Angle of Depression When looking DOWN to an object, the angle of depression is formed by an observer’s line of sight and a horizontal line. The angle of depression is congruent to the angle of elevation because they are alternate interior angles.

Examples Casey sights the top of an 84 ft tall lighthouse at and angle of elevation of 58°. If Casey is 6 feet tall, how far is he standing from the base of the lighthouse? A lifeguard is sitting on a platform, looking down at a swimmer in the water. If the lifeguard’s line of sight is 8 ft above the ground and the angle of depression to the swimmer is 18°, how far away is the swimmer from the lifeguard?

Review

Friday 05/10 Warm Up

You Try! The angle of elevation from a kicker’s foot on the football field to the top of the goal post bars is 17°. If he is standing 131 ft. from the base of the goal post, how tall is the goal post? A pilot in a helicopter spots a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is 1200 ft., what is the altitude of the helicopter?

Review

SOH CAH TOA Task Cards

Monday 05/13 Warm Up Elijah is looking up to the top of the Washington Monument. If the monument is 555 ft. tall and the angle of elevation from the point on the ground where Elijah is standing to the top is 74°, how far is he standing from the base of the monument? The angle of depression from an airplane to the TOP of an air traffic control tower is 56°. If the tower is 320 feet tall and the airplane is flying at an altitude of 7,450 ft., how far away is the airplane from the control tower?

Motivational Monday

Triangle Guide Book

Study Guide!

Turn in: Assignment Sheet Workbook Study Guide TEST DAY!

Wednesday 05/15 Warm Up Find the dilated coordinates with the given scale factor. S(3, -5), T(0, -2), U(-3, -5), V(0, -8) Scale factor = 4 S’:____ T’:____ U’:____ V’:____ F(-6, -5), G(3, -4), H(3, -7) Scale factor = ⅛ F’:____ G’:____ H’:____