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Page 1: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Page 2: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed

C

Page 3: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Corresponding angles are congruent

AND Corresponding sides

are proportional in length

Minimum Conditions:1. AA2. SAS3. SSS

Page 4: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

ActivityTake 10 minutes.Use graph paperDraw a right triangleDraw the altitude from the right angleProve that 3 similar triangles are formed

Page 5: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Activity 1: Birds of a feather stick together! Problem: Mother Nature Enraged!

Page 6: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.

leg

projection

leg

projection

Page 7: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Using the lengths of the corresponding sides of the triangles formed, we can determine the ratios and from this determine certain geometric properties

Page 8: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Information we have or need:1. Measurement of leg2. Measurement of projection3. Measurement of hypotenuse

Page 9: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

projection leg

leg hypotenuse

leg

proj

leg

proj

Page 10: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

projection leg

leg hypotenuse

leg

proj

leg

proj

Page 11: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

In a right triangle the length of the leg of a right triangle is the geometric mean between the length of its projection on the hypotenuse

Page 12: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Worksheet hand out on Property 1

Page 13: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Information we have or need:1. Altitude2. 2 segments that determine hypotenuse

i.e. projections

Page 14: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

projection altitude

altitude projection

proj proj

altitude

Page 15: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

In a right triangle the length of the altitude drawn from the right angle is the geometric mean of the length of the two segments that determine the hypotenuse

Page 16: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Worksheet on Property 2

Page 17: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Information we have or need:1. Hypotenuse2. Altitude3. Length of legs

Page 18: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

hypotenuse altitude leg leg

leg leg

hypotenuse

altitude

Page 19: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

In a right triangle, the product of the length of the hypotenuse and its corresponding altitude is equal to the product of the lengths of the legs.

Page 20: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Hand out on property 3

Page 21: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Pythagorean Theorem

Page 22: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Visions page 182, numbers 1,2,3,4

Page 23: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.

or

Page 24: By drawing the altitude from the right angle of a right triangle, three similar right triangles are formed C

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

Similar Right Triangles

7.4 Similarity in Right Triangles In this lesson we will learn the relationship between different parts of a right triangle that has an altitude drawn

9.1 – Similar Right Triangles. Theorem 9.1: If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar

7-4 Similarity in Right Triangles Students will use the special case of drawing an altitude in right triangles to find similar triangles. They will also

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7.3 Similar Right Triangles Geometry. Objective(s) Students will understand geometric concepts and use properties of the altitude of a right triangle

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Special Right Triangles and Trigonometry - Wikispaceschoong.wikispaces.com/.../Special+Right+Triangles+and+Trigonome… · Special Right Triangles and ... special right triangles

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Review May 16, 2008. Right Triangles The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the

4-6 Congruence in Right Triangles 1 card. Vocabulary Right Triangles

8-4 Similarity in Right Triangles · 2003. 4. 13. · Theorem 8-3 Altitude Similarity Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles

Chapter 11 Right Triangles - Hanlon Mathhanlonmath.com/pdfFiles/591Ch11RightTriangles-Trigtrig.pdf · Chapter 11 Right Triangles ... In this case, we will draw an altitude to the

right triangles Application

Use Similar Right Triangles Ch 7.3. Similar Right Triangle Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles

6.6 Similar Triangle Right Triangles · Similar Triangles in Right Triangles 6.6 ... triangles and write and solve proportions as needed. 6.6 ... Right triangles,

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Trigonometry of Right Triangles - Cal State LA | We …...Trigonometry+of+Right+Triangles+++++Page1|9+ Trigonometry of Right Triangles Right Triangles A right triangle, as the one

SPECIAL RIGHT TRIANGLES CHEAT SHEET 45-45-90 TRIANGLEmsubmathing.weebly.com/uploads/3/8/0/6/38068469/... · Find the length of the triangles altitude. 11. The altitude of an equilateral

7.4.1 SPECIAL RIGHT TRIANGLES Chapter 7: Right Triangles and Trigonometry

Geometric Mean and Proportional Right Triangles - The Math Planemathplane.com/yahoo_site_admin/assets/docs/altitude... · 2017. 3. 25. · Geometric Mean and Proportional Right Triangles

Tutorials--Right Triangles

9.2 Special Right Triangles - WordPress.com · 09.04.2018 · 9.2 Special Right Triangles There are two types of special right triangles; 45-45-90 Triangles and 30-60-90 Triangles

Special Right Triangles 45:45:90 Right Triangles

6.6 Similar Triangle Right Triangles · 6.6 (2) highlighter Similarity: Right triangles, altitudes, and similarity Recall that an altitude of a triangle is a perpendicular line segment

SPECIAL RIGHT TRIANGLES:

Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Special Right Triangles 30:60:90 Right Triangles

Right Triangles Special Right Trianglessmacmathgeometry.weebly.com/uploads/1/9/2/5/19254419/g8... · 2019-02-01 · Right Triangles – Special Right Triangles Homework Section 8.4

Geometric Mean and Proportional Right Triangles...Right Triangles: Altitude, Geometric Mean, and Pythagorean Theorem Geometnc mean of divided hvpotenuse is the length of the altitude

10.1 Similar Right Triangles Learning Objective: To recognize relationships among the triangles formed by the altitude to the hypotenuse of right triangle,

Special Right Triangles

7... · Using the Right Triangle Altitude Theorem, separate each of the right triangles below and then write a similarity statement showing the correspondence between all three triangles