13.3 Special Right Triangles p 709

Slides:



Advertisements
Similar presentations
Report by Jennifer Johnson
Advertisements

4-5 Isosceles and Equilateral Triangles Learning Goal 1. To use and apply properties of isosceles and equilateral triangles.
The World Of Triangles Mohamed Attia Mohamed copyrigh.mohamedattia blogspot.com.
Lesson 4 Triangle Basics.
Warm Up for Section 1.1 Simplify: (1). (2). Use the triangle below to answer #3, #4: (3). Find x. (4). If a = 5, b = 3, find c. 40 o a b c xoxo.
Angles and their measurements. Degrees: Measuring Angles We measure the size of an angle using degrees. Example: Here are some examples of angles and.
SPI Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons.
Special Right Triangles
Geometry’s Most Elegant Theorem Pythagorean Theorem Lesson 9.4.
10.1 Triangles. Acute Triangle Not Acute Triangles.
Lesson 56: Special Right Triangles
Unit 6 Lesson 2 Special Right Triangles
The World Of Triangles. Triangles A triangle is a 3- sided polygon. Every triangle has three sides and three angles. When added together, the three angles.
Lesson 9.4 Geometry’s Most Elegant Theorem Objective: After studying this section, you will be able to use the Pythagorean Theorem and its converse.
More About Triangles § 6.1 Medians
TRIANGLES (There are three sides to every story!).
Special Right Triangles
Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form
10/1/ : Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.
Lesson 4-5: Isosceles & Equilateral Triangles Vocab Legs Base Angles Equiangular Bisects The congruent sides of an isosceles ∆ Congruent angles opposite.
4.5 Isosceles and Equilateral Triangles. Isosceles Triangles At least two sides are of equal length. It also has two congruent angles. Base Angles Base.
Isosceles and Equilateral Triangles Section 5-1. Isosceles Triangle A triangle with at least two congruent sides. Leg Leg Base Vertex Angle Base Angles.
Properties of Special Triangles 4-5 Objective: To use and apply properties of isosceles and equilateral triangles.
Lesson Handout #1-49 (ODD). Special Right Triangles and Trigonometric Ratios Objective To understand the Pythagorean Theorem, discover relationships.
The World Of Triangles. Triangles A triangle is a 3- sided polygon. Every triangle has three sides and three angles. When added together, the three angles.
Investigation 4.2 AMSTI Searching for Pythagoras.
Isosceles Triangle ABC Vertex Angle Leg Base Base Angles.
Special Right Triangles
Holt CA Course Triangles Vocabulary Triangle Sum Theoremacute triangle right triangleobtuse triangle equilateral triangle isosceles triangle scalene.
Warm Up. 9.4 Geometry’s Most Elegant Theorem Pythagorean Theorem.
Triangle Sum Theorem The sum of the angle measures in a triangle is 180 degrees.
Unit 6 Lesson 3 Special Right Triangles
Why does the line y = x only have one slope? What is true about all of the triangles? How does this relate to Pythagorean Theorem?
Warm Up # 4 Classify and name each angle. 1 ab c d.
Special Right Triangles. Right triangles have one 90 o angle The longest side is called the HYPOTENUSE It is directly across from the 90 o The other sides.
PSAT MATHEMATICS 9-J Triangles G EOMETRY 1. Angles of a Triangle In any triangle, the sum of the measures of the three angles is _______. 2.
– Use Trig with Right Triangles Unit IV Day 2.
Warm-Up If a triangle has two side lengths of 12 and 5, what is the range of possible values for the third side? 2.
Section Goal  Find the side lengths of 45 ˚ -45 ˚ -90 ˚ triangles.
The World Of Triangles Free powerpoints at
Lesson 35: Special Right Triangles and the Pythagorean Theorem
Isosceles, Equilateral, Right Triangles
Objectives Justify and apply properties of 45°-45°-90° triangles.
Complete “You Try” section p.11 in your workbook!
Warm Up [On back counter]
Bell Work: List 3 triangle congruence theorems
Objectives Prove theorems about isosceles and equilateral triangles.
Standard:9 geometry triangles
The World Of Triangles Free powerpoints at
Special Right Triangles
Chapter 4 Section 4.1 – Part 1 Triangles and Angles.
Triangles A polygon with 3 sides.
4.1 Triangles and Angles.
Warm up: Think About it! If the red, blue and green squares were made of solid gold; would you rather have the red square or both the blue and green square?
Discovering Special Triangles
Day 99 – Trigonometry of right triangle 2
Class Greeting.
7.2 Isosceles and Equilateral Triangles
Mod 15.2: Isosceles and Equilateral Triangles
Pythagorean Theorem a²+ b²=c².
Right Triangles Unit 4 Vocabulary.
Lesson 14.2 Special Triangles pp
9.2 A diagonal of a square divides it into two congruent isosceles right triangles. Since the base angles of an isosceles triangle are congruent, the measure.
Chapter 4 Congruent Triangles.
GEOMETRY’S MOST ELEGANT THEOREM Pythagorean Theorem
Warm-up Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. a = b = a = 2.
The World Of Triangles Powerpoint hosted on
Equilateral TRIANGLES
Right Triangles TC2MA234.
7.3 Special Right Triangles
Presentation transcript:

13.3 Special Right Triangles p 709 CCSS – SRT 8.1 Derive and use the trigonometric ratios for special right triangles

Warm up What is an isosceles triangle? What do you mean by complementary angles? What is an Isosceles Triangle Theorem What is the Pythagorean Theorem?

answers An isosceles triangle has at least 2 congruent sides. Two angles whose measures have a sum of 90o. If two sides of a triangle are congruent, then the angles opposite the sides are congruent.

Explore 1 Investigating an isosceles Right Triangle Discover relationships that always apply in an isosceles right triangle. A. Draw an isosceles right triangle ABC with legs measures x and right angle at C. Identify the base angles, and use the fact that they are complementary to write an equation relating their measures. B. Use the Isosceles Triangle Theorem to write a different equation relating the base angle measures. C. What must the measures of the base angles be? Why?

answers A. Base angles are / A and /B m/ A + m /B = 90o B. m/ A = m /B C. 45o

Use the Pythagorean Theorem to find the length of the hypotenuse in terms of the length of each leg, x.

answer AB2 = x2 + x2 AB2 = 2x2 AB = x√2

Reflections 1. Is it true that if you know one side length of an isosceles right triangle, then you know all the side lengths? Explain. 2. Suppose you draw the perpendicular from C to AB. Explain how to find the length of CD.

Explore 2 : Investigating another special right triangle Discover relationships that always apply in a right triangle formed as half of an equilateral triangle.

ΔABD is an equilateral triangle and BC is a perpendicular from B to AD ΔABD is an equilateral triangle and BC is a perpendicular from B to AD. Determine all three angle measures in ΔABC.

Reflections 1. What is the numerical ratio of the side lengths in a right triangle with acute angles that measure 30o and 60o? Explain.

2. A student has drawn a right triangle with a 60o angle and a hypotenuse of 6. He has labeled the other side lengths as shown. Explain how you can tell at a glance that he has made an error and how to correct it.