Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into...

17
Geom93SimilarityInRightTriangles.notebook April 02, 2018 Geometry P39 93 Similarity in Right Triangles 1. 2. 3. 2x 2 = 50 Review Simplify or Solve...

Transcript of Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into...

Page 1: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Geometry

P39 9­3 Similarity in Right Triangles

1. 2. 3. 2x2 = 50

Review ­ Simplify or Solve...

Page 2: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Review Use Pythagorean Theorem to find x.a2 + b2 = c2

3

4 x

3

5x 4 5

x

Page 3: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

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

Find the geometric mean of the two numbers.

Page 4: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Geometric Mean ­Proportions in which the means are equal.

x

Corollary 1 to Theorem ­ (The Heartbeat Theorem)

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Page 5: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Find yUse Pythagorean Theorem to find x.a2 + b2 = c2

(The Heartbeat Theorem)

(The Heartbeat Theorem)Solve for x and y.

Page 6: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Solve for x and y. (The Heartbeat Theorem)

Corollary 2 to Theorem ­  (The Hockey Stick Theorem)

The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.

Page 7: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Find X

(The Hockey Stick Theorem)Use Pythagorean Theorem to find x.a2 + b2 = c2

Solve for x and y. (The Hockey Stick Theorem)

Page 8: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

At a golf course, Maria drove her ball 192 yd straight toward the cup.  Her brother Gabriel drove his ball straight 240 yd, but not toward the cup.  The diagram shows the results.  Find x and y, their remaining distances from the cup.

Page 9: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

HW#44  9­3 WS

Please put your name and class period at the top ofthe homework.  Also include the homework number.

Page 10: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Page 11: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

a2 + b2 = c2

Page 12: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Identify the similar triangles.

Find the value of x.

Find the value of each variable.

Page 13: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Page 14: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height h of the roof.

To find the cost of installing a rock wall in your school gymnasium, you need to find the height of the gym wall. You use a cardboard square to line up the top and bottom of the gym wall. Your friend measures the vertical distance from the ground to your eye and the horizontal distance from you to the gym wall. Approximate the height of the gym wall.

Page 15: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Page 16: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Redraw all three triangles and complete each statement.

Page 17: Geometry · Theorem The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. Find the

Geom9­3SimilarityInRightTriangles.notebook April 02, 2018

Really Complex Problem


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.

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.

masdwijanto.files.wordpress.com. hypotenuse d. altitudes Construct an isosceles triangle that contains a 450 vertex angle. Construct a right, scalene triangle. Construct an obtuse

masdwijanto.files.wordpress.com. hypotenuse d. altitudes Construct an isosceles triangle that contains a 450 vertex angle. Construct a right, scalene triangle. Construct an obtuse

9-2 Tuesday 3/19 or Wednesday 3/20. Bell Work Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse.

9-2 Tuesday 3/19 or Wednesday 3/20. Bell Work Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse.

Welcome! [] · 30-60-90 Triangle Investigation Step 1: Find the length of the hypotenuse for each triangle below. Step 2: use the Pythagorean theorem to find the long leg of each

Welcome! [] · 30-60-90 Triangle Investigation Step 1: Find the length of the hypotenuse for each triangle below. Step 2: use the Pythagorean theorem to find the long leg of each

PT Lesson Plan Final RWood-2 - WordPress.com · •!Argue whether a triangle is a right triangle using the Pythagorean Theorem and the three given sides •!Define the hypotenuse

PT Lesson Plan Final RWood-2 - WordPress.com · •!Argue whether a triangle is a right triangle using the Pythagorean Theorem and the three given sides •!Define the hypotenuse

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

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

Find the hypotenuse in a right triangle with legs a = 3 and b = 4. 55 Exercise.

Find the hypotenuse in a right triangle with legs a = 3 and b = 4. 55 Exercise.

Bell Work: Find the hypotenuse of a triangle with leg lengths of 5 and 6 cm.

Bell Work: Find the hypotenuse of a triangle with leg lengths of 5 and 6 cm.

Pythagorean Theorem. Right Triangle Hypotenuse Legs Pythagorean Theorem Radical/Radicand Square Root VOCABULARY.

Pythagorean Theorem. Right Triangle Hypotenuse Legs Pythagorean Theorem Radical/Radicand Square Root VOCABULARY.

13.1 Right Triangle Trigonometry - ClassZone · Page 1 of 2 13.1 Right Triangle Trigonometry 769 ... the length of the hypotenuse is: 32+ 42= 25 = 5 ... the altitude of a kite in

13.1 Right Triangle Trigonometry - ClassZone · Page 1 of 2 13.1 Right Triangle Trigonometry 769 ... the length of the hypotenuse is: 32+ 42= 25 = 5 ... the altitude of a kite in

7.3 Use Similar Right Triangles€¦ · In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length Of each leg Of

7.3 Use Similar Right Triangles€¦ · In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length Of each leg Of

5.5 Proving Triangle Congruence by SSS - Weeblyederushe.weebly.com/uploads/3/7/6/5/37655305/geo_tb_5.5.pdf · Section 5.5 Proving Triangle Congruence by SSS 265 Using the Hypotenuse-Leg

5.5 Proving Triangle Congruence by SSS - Weeblyederushe.weebly.com/uploads/3/7/6/5/37655305/geo_tb_5.5.pdf · Section 5.5 Proving Triangle Congruence by SSS 265 Using the Hypotenuse-Leg

1. PYTHAGOREAN THEOREM - · PDF file1. PYTHAGOREAN THEOREM In a right triangle one of the angles of the triangle measures 90. The side opposite the right angle is called the hypotenuse.

1. PYTHAGOREAN THEOREM - · PDF file1. PYTHAGOREAN THEOREM In a right triangle one of the angles of the triangle measures 90. The side opposite the right angle is called the hypotenuse.

By: PATRIES NAGBE nextbackhome. What is a right triangle ? What is a right triangle ? What are the parts of a right triangle ? What is a hypotenuse.

By: PATRIES NAGBE nextbackhome. What is a right triangle ? What is a right triangle ? What are the parts of a right triangle ? What is a hypotenuse.

Home - Warren County Public Schools · 2017-12-20 · 8-1 The Pythagorean Theorem Theorem 8-1 Pythagorean Theorem — (hypotenuse)2 Theorem If a triangle is a right triangle, then

Home - Warren County Public Schools · 2017-12-20 · 8-1 The Pythagorean Theorem Theorem 8-1 Pythagorean Theorem — (hypotenuse)2 Theorem If a triangle is a right triangle, then

4 Triangles - study-point.com · triangles on each side of the perpendicular are similar to the whole triangle and to each other. In a right triangle, the square of the hypotenuse

4 Triangles - study-point.com · triangles on each side of the perpendicular are similar to the whole triangle and to each other. In a right triangle, the square of the hypotenuse

1.Leg – One of 2 sides of a right triangle 2.Hypotenuse – the longest side of a right triangle 3.Triangle-a 3-sided polygon 4.Polygon-a 2-D figure, has.

1.Leg – One of 2 sides of a right triangle 2.Hypotenuse – the longest side of a right triangle 3.Triangle-a 3-sided polygon 4.Polygon-a 2-D figure, has.

mrsaiellomath.weebly.commrsaiellomath.weebly.com/uploads/3/1/4/2/31426561/... · 2018. 3. 7. · of right triangle ABC, altitude BD divides hypotenuse AC into segments with lengths

mrsaiellomath.weebly.commrsaiellomath.weebly.com/uploads/3/1/4/2/31426561/... · 2018. 3. 7. · of right triangle ABC, altitude BD divides hypotenuse AC into segments with lengths

New Document1 - The Asian School · 2019. 12. 4. · The base Of a right-angled triangle measures 4cm and its hypotenuse measures 5cm. find the area Of the triangle. ... If the side

New Document1 - The Asian School · 2019. 12. 4. · The base Of a right-angled triangle measures 4cm and its hypotenuse measures 5cm. find the area Of the triangle. ... If the side

Dr. Fowler CCM1A EXAM REVIEW 01. Pythagorean Theorem leg hypotenuse The hypotenuse is always the longest side of a right triangle and is always opposite.

Dr. Fowler CCM1A EXAM REVIEW 01. Pythagorean Theorem leg hypotenuse The hypotenuse is always the longest side of a right triangle and is always opposite.