Pythagorean Theorem.

Slides:



Advertisements
Similar presentations
Jeopardy Review Find the Missing Leg / Hypotenuse Pythagorean Theorem Converse Distance Between 2 Points Everybody’s Favorite Similar T riangles Q $100.
Advertisements

Quiz Review 7.1,7.2, and 7.4.
Honors Geometry Section 5.4 The Pythagorean Theorem
Pythagorean Theorem, Distance Formula and Midpoint Formula.
A number that has a whole number as its square root is called a perfect square. The first few perfect squares are listed below. Slide
The Pythagorean Theorem A tool for right triangle problems only.
Warm up Write the equation of the line that: 1. Is parallel to y = 3 and goes through the point (2, -4) 2. Is perpendicular to y = 2x + 6 and goes through.
Then/Now You have already found missing measures of similar triangles. (Lesson 6–7) Use the Pythagorean Theorem to find the length of a side of a right.
Direct Analytic Proofs. If you are asked to prove Suggestions of how to do this Two lines parallel Use the slope formula twice. Determine that the slopes.
Geometry Section 9.4 Special Right Triangle Formulas
Objective The student will be able to: use the Pythagorean Theorem Designed by Skip Tyler, Varina High School.
Pythagorean Theorem As posted by: oints/math/pythagorean.html.
Sec 6.6 Pythagorean Theorem. Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! leg hypotenuse - always opposite.
The Pythagorean Theorem
Intro screen.
Learning Target: I can solve problems involving the Pythagorean Theorem. For Right Triangles Only! leg hypotenuse - always opposite the right angle.
6.7 Polygons in the Coordinate Plane
Classifying Triangles By Angles Acute: all three angles are less than 90 ◦ Obtuse: one angle is greater than 90 ◦ Right: one angle measure is 90 ◦ By.
Chapter 8: Right Triangles & Trigonometry 8.2 Special Right Triangles.
Special Right Triangles Trigonometric Ratios Pythagorean Theorem Q: $100 Q: $200 Q: $300 Q: $400.
Warm up r = -3 k = -3 x = – 6r = 2r k – 5 = 7k + 7
The Distance Formula & Pythagorean Theorem Day 90 Learning Target : Students can find the distance between 2 points using the distance formula.
ENTRY TASK – Find the value of x and y. 3. Find the geometric mean between 3 and
SineCosineTangentPythagoreanTheorem Mixed Word Problems(Regents)
Warm up Solve – 6r = 2r k – 5 = 7k (x + 4) = 6x r = -3 k = -3 x = 2.
Sec 6.6 Pythagorean Theorem (Leg1) 2 + (leg2) 2 = (Hyp) 2 hypotenuse Leg 2 Leg 1.
Warm up Find the missing side.. Daily Check Review Homework.
Warm up Solve – 6r = 2r k – 5 = 7k (x + 4) = 6x r = -3 k = -3 x = 2.
Warm up Solve – 6r = 2r k – 5 = 7k (x + 4) = 6x r = -3 k = -3 x = 2.
Notes Over 10.1 Finding the Distance Between Two Points Find the distance between the two points.
Pythagorean Theorem Triangles: 3 sides, 3 angles sum of angles = 180
SOL 8.10 Pythagorean Theorem.
Warm-up Use the Pythagorean theorem to find the missing length of the right triangle. Round to the nearest tenth Determine whether the given.
The Pythagorean Theorem
Warm up Given: Point A (3, -2) and Point B (9, 4)
The Pythagorean Theorem
Before: April 12, 2016 What is the length of the hypotenuse of
The Pythagorean Theorem
A man and his wife have three sons, and every one of the sons has a sister… How many people are there in the family? A. 6 B. 8 C. 10 D. 12.
Pythagorean Theorem Converse
Warm Up Use the figure for problems 1 and 2. round to the nearest hundredth 1) Find the height a of the triangle c 10 8 a 6 9 2) Find the length of side.
The Pythagorean Theorem
Apply the Distance and Midpoint Formulas
Warm-up Use the Pythagorean theorem to find the missing length of the right triangle. Round to the nearest tenth Determine whether the given.
Objective- To solve problems involving the Pythagorean Theorem.
Warm up What is the equation of the line that goes through (1, 4) and (5, 12)? What is the distance between (1, 4) and (5, 12)? What is the equation of.
Splash Screen.
Pythagorean Theorem.
Solve each equation Solve each equation. x2 – 16 = n = 0
Distance Formula Q1 of 13 Find the distance between:
Objective- To solve problems involving the Pythagorean Theorem.
Pythagorean Theorem.
The Distance Formula Use this formula to find the distance between the following two points.
The Distance Formula & Pythagorean Theorem
Warm up r = -3 k = -3 x = – 6r = 2r k – 5 = 7k + 7
PROVING A TRIANGLE IS AN ISOSCELES TRIANGLE
PROVING A TRIANGLE IS AN ISOSCELES TRIANGLE
Warm up What is the equation of the line that goes through (1, 4) and (5, 12)? What is the distance between (1, 4) and (5, 12)? What is the equation of.
Splash Screen.
Pythagorean Theorem OR.
If a triangle is a RIGHT TRIANGLE, then a2 + b2 = c2.
Pythagorean Theorem, its Converse and the coordinate system
Sine and Cosine Rule s.small.
Warm up r = -3 k = -3 x = – 6r = 2r k – 5 = 7k + 7
Objective- To solve problems involving the Pythagorean Theorem.
The Pythagorean Theorem
The Pythagorean Theorem
Pythagorean Theorem.
Pythagorean Theorem.
Pythagorean Theorem & Its Converse
Presentation transcript:

Pythagorean Theorem

Classwork Round to the nearest tenths. Worksheet

Pythagorean Theorem Word Problems A square has a diagonal with length of 20 cm. What is the measure of each side? Round to the nearest tenths. x = 14.1 cm

Pythagorean Theorem Word Problems A 25 foot ladder is leaning against a building. The foot of the ladder is 15 feet from the base of the building. How high is the top of the ladder along the building? Round to the nearest tenths. x = 20 ft

Pythagorean Theorem Word Problems Ashley travels 42 miles east, then 19 miles south. How far is Ashley from the starting point? Round to the nearest tenths. x = 46.1 miles

Pythagorean Theorem Word Problems What is the length of the altitude of an equilateral triangle if a side is 12 cm? Round to the nearest tenths. x = 10.4 cm

The Distance Formula

D = 3.16 Example Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D = 3.16

Example Find the distance between the points, (10, 5) and (40, 45). Round to the nearest hundredths. D = 50

3. Find the distance between the points. Round to the nearest tenths. 3.6

4. Find the distance between the points. Round to the nearest tenths. 5.4

4. Find the distance between the points. Round to the nearest tenths. 5

Classifying Triangles by Sides Equilateral – 3 congruent sides Isosceles – 2 congruent sides Scalene – No sides congruent Congruent = Same Distance

Classwork / Homework Triangles Task

Conclusions Parallel Same slope means sides are parallel Opposite reciprocal slopes mean perpendicular segments (90) Distance Same distance means segments are congruent