1 PROPORTIONS REVIEW ALTITUDE FROM HYPOTENUSE FORMS SIMILAR TRIANGLES PROBLEM 1a PROBLEM 1b PROBLEM 2 PROBLEM 3 PROBLEM 4 PROBLEM 5 PROBLEM 6 STANDARDS.

Slides:



Advertisements
Similar presentations
SPECIAL SEGMENTS IN A TRIANGLE MEDIANS ARE PROPORTIONAL PROBLEM 6
Advertisements

PROBLEM 1A PROBLEM 2A PROBLEM 3A PROBLEM 4A PROBLEM 1B PROBLEM 4B PROBLEM 2B PROBLEM 3B TRIANGLES AS POLYGONS: CLASSIFICATION PRESENTATION CREATED BY.
PROPORTIONS SSS SIMILARITY PARALLEL TRANSVERSALS PROBLEM 1 PROBLEM 2
1 30°-60°-90° TRIANGLE 45°-45°-90° TRIANGLE PROBLEM 1 PROBLEM 2 PROBLEM 4 PROBLEM 5 Standard 20 END SHOW PRESENTATION CREATED BY SIMON PEREZ. All rights.
1 Basic Polygon Definitions Interior Angle Sum Theorem Exterior Angle Sum Theorem PROBLEM 1aPROBLEM 1b PROBLEM 2aPROBLEM 2b PROBLEM 3aPROBLEM 3b PROBLEM.
1 INTRODUCTION LAW OF SINES AND COSINES LAW OF SINES LAW OF COSINES PROBLEM 1b PROBLEM 1a PROBLEM 2a PROBLEM 2b PROBLEM 4b PROBLEM 4a PROBLEM 3b PROBLEM.
SEGMENT ADDITION POSTULATE
1 The sum of 2 sides of the triangle greater than the other side? Ordering the angles of a triangle? Ordering the sides of a triangle? SAS Inequality.
1 CPCTC SIDE-ANGLE-SIDE ANGLE-ANGLE-SIDE PROBLEM 1 SIDE-SIDE-SIDE PROBLEM 3 ANGLE-SIDE-ANGLE Standards 4 and 5 SUMMARY: CONGRUENCE IN TRIANGLES SUMMARY:
Chapter 9 Geometry © 2008 Pearson Addison-Wesley. All rights reserved.
Section 9-3 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.
1 SLOPE FORMULA SLOPE FORMULA: PROBLEMS SLOPE: RUN VS RISE. PROBLEMS FALLING OR RISING LINES? SLOPE CASES PARALLEL VS PERPENDICULAR PARALLEL VS SKEW AND.
CONGRUENT AND SIMILAR FIGURES
1 PROBLEM 1A PROBLEM 2A PROBLEM 3A PROBLEM 4A PROBLEM 1B PROBLEM 4B PROBLEM 2B PROBLEM 3B TRIANGLES AS POLYGONS: CLASSIFICATION Standards 4 and 5 REFLEXIVE,
4.1 Quadrilaterals Quadrilateral Parallelogram Trapezoid
1 Standards 7, 8, 10 Review Classification of Triangles Review Area of Triangle Area of an EQUILATERAL TRIANGLE given the side Area of an EQUILATERAL.
1 PROPERTIES OF EQUALITY Standard 1 SOLUTION OF EQUATIONS INCLUDING ABSOLUTE VALUE EQUATIONS EQUATIONS LEVEL 1 EQUATIONS LEVEL 2 EQUATIONS LEVEL 3 EQUATIONS.
1 Review Parallelogram Properties Review Rectangle Properties Review Square Properties Finding the Area of a Parallelogram Finding the Area of Rectangles.
1 Standards 7, 8 Review Rhombus Properties Review Isosceles Trapezoid Properties Review Trapezoid Properties Finding the Area of a Triangle PROBLEM 1 PROBLEM.
ANGLES FORM BY A TRANSVERSAL PARALLEL LINES CUT BY A TRANSVERSAL
Standard 20 30°-60°-90° TRIANGLE PROBLEM 1 PROBLEM 2
© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 9-4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.
Aim: Triangle Congruence – Hyp-Leg Course: Applied Geometry Do Now: Aim: How to prove triangles are congruent using a 5 th shortcut: Hyp-Leg. In a right.
Right Triangles and Trigonometry
Similar Right Triangles
9.3 Altitude-On-Hypotenuse Theorems Objective: After studying this section, you will be able to identify the relationships between the parts of a right.
A B C D Lesson 9.3. AB D C A D C B D A C B Three similar triangles: small, medium and large. Altitude CD drawn to hyp. of △ ABC Three similar triangles.
Similarity in Right Triangles
Section 5-2 Bisectors in Triangles. Vocabulary Distance from a point to a line: the length of the perpendicular segment from the point to the line.
Chapter 7: Proportions and Similarity
9.1 Similar Right Triangles Geometry Mrs. Spitz Spring 2006.
Special Topics Eleanor Roosevelt High School Chin-Sung Lin.
9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)
LM Jeopardy Geometric Means Proportions Similar figures Parallel Lines Special Segments $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 Final Jeopardy.
7.3 Similar Right Triangles Geometry. Objective(s)  Students will understand geometric concepts and use properties of the altitude of a right triangle.
Similar Figures. Square Limit by M.C. Escher Escher used a pattern of squares and triangles to create Square Limit. These two triangles are similar. Similar.
1 RATIOS IN RIGHT TRIANGLES OPPOSITE SIDE? ADJACENT SIDE? HYPOTENUSE? SINE? COSINE? TANGENT? Standards 15, 18, 19 END SHOW PRESENTATION CREATED BY SIMON.
Similar - Two figures are similar figures if they have the same shape but they may not be the same size. The symbol ~ means similar. Corresponding parts.
Chapter 7 Similarity.
Warm Up 1.Name a chord 2.What term describes
RATIOS IN RIGHT TRIANGLES OPPOSITE SIDE? ADJACENT SIDE? HYPOTENUSE? SINE? COSINE? TANGENT? INVERSE OF TRIGONOMETRIC RATIOS PROBLEM 1a PROBLEM 1b PROBLEM.
9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)
9.1 Similar Right Triangles Geometry. Objectives  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of.
Lesson 7.3 Using Similar Right Triangles Students need scissors, rulers, and note cards. Today, we are going to… …use geometric mean to solve problems.
Key Learning  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of a right triangle.  Use a geometric mean.
9.1 Similar Right Triangles Geometry Mrs. Blanco.
9.1 Similar Right Triangles
9.1 Similar Right Triangles
6.5 Prove Triangles Similar by SSS and SAS
9.1 Similar Right Triangles
Warm UP.
L21_Ratios and Proportions Eleanor Roosevelt High School Chin-Sung Lin
7-5: Parts of Similar Triangles
9.1 Similar Right Triangles
EXAMPLE 3 Use the Hypotenuse-Leg Congruence Theorem Write a proof.
9.1 Similar Right Triangles
Similarity, Congruence, & Proofs
7.1 Ratio and Proportions.
9.1 Similar Right Triangles
Similar Figures Susan Phillips Lee’s Summit, MO.
Similar Figures.
9.3 Altitude-On-Hypotenuse Theorems
Altitudes–On- Hypotenuse Theorem
Similar Right Triangles
Topic 7: Similarity 7-1: Properties of Proportions
DO NOW.
Postulates and Theorems to show Congruence SSS: Side-Side-Side
9.1 Similar Right Triangles
Right Triangles with an altitude drawn.
Objectives Apply SSS to construct triangles and solve problems.
Presentation transcript:

1 PROPORTIONS REVIEW ALTITUDE FROM HYPOTENUSE FORMS SIMILAR TRIANGLES PROBLEM 1a PROBLEM 1b PROBLEM 2 PROBLEM 3 PROBLEM 4 PROBLEM 5 PROBLEM 6 STANDARDS 4, 5, 14, 15 END SHOW PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

2 Standard 4: Students prove basic theorems involving congruence and similarity. Los estudiantes prueban teoremas básicos de congruencia y semejanza. Standard 5: Students prove triangles are congruent or similar and are able to use the concept of corresponding parts of congruent triangles. Los estudiantes prueban que los triangulos son congruentes o semejantes y son capaces de usar el concepto de partes correspondientes en triángulos congruentes. Standard 14: Students prove the Pythagoream Theorem. Los estudiantes prueban el Teorema de Pitágoras. Standard 15: Students use the Pythagoream Theorem to determine distance and find missing lenghts of sides of right triangles. Los estudiantes usan el Teorema de Pitágoras para determinar distancia y el lado faltante de un triángulo rectangulo. PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

3 A D A and D are the EXTREMES B C B and C are the MEANS Cross-multiplying: (A)(D)=(C)(B)The product of the MEANS is equal to the product of the EXTREMES PROPORTIONS REVIEW = A D B C = A D B C = PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

4 x x = Find the GEOMETRIC MEAN of 10 and 40: x x Cross-multiplying (10)(40)=(x)(x) Applying symmetric property x = |x|=20x=20 and x=-20 = PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

5 x x6 24 = Find the GEOMETRIC MEAN of 6 and 24: x x6 24 Cross-multiplying (6)(24)=(x)(x) Applying symmetric property x = |x|=12x=12 and x=-12 = PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

6 D A B C How many similar triangles Altitud CD in ABC form? STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

7 A D B C A C B A D C C DB STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

8 AD AC A B A D C CB DC STANDARDS 4, 5, 14, 15 C PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

9 A CB A D C AC AD AB AC STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

10 A C B A D C CB DC AB AC STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

11 A D C C DB AD DC DB AD DC AC CB AC CB DC DB STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

12 A C B C DB AC CD CB DB AC CD AB CB AB CB DB STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

13 A C B A D C C DB AC AD CB DC AC AD AB AC AB AC CB DC AD CD DC DB AD CD AC CB AC CB DC DB AC CD CB DB AC CD AB CB AB CB DB STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

14 A D B C A C A D C DB C B AC CD CB DB AC CD AB CB AB CB DB ACB CDB AD CD DB AD CD AC CB AC CB DC DB ADC CDB AC AD CB DC AC AD AB AC AB AC CB DC ACB ADC STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

15 z y x STANDARDS 4, 5, 14, 15 Find the value for x, y and z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

16 z y x 17 8 z z 8 8 x y x+y 1. STANDARDS 4, 5, 14, 15 Find the value for x, y and z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

17 8 x x + 8 = x + 64 = x = |x|=15 x=15 and x= STANDARDS 4, 5, 14, 15 Find the value for x, y and z: z y x 17 8 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

x= 15z y (17) z = (8)(17) 15 z z = STANDARDS 4, 5, 14, 15 Find the value for x, y and z: = z = z y x 17 8 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

x= 15z y y (8) y = (8)(8) STANDARDS 4, 5, 14, 15 Find the value for x, y and z: = y = y = 4.3. z y x 17 8 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

20 10 x 5 y z 2. STANDARDS 4, 5, 14, 15 Find the value for x, y and z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

21 2. zz x x y y STANDARDS 4, 5, 14, 15 Find the value for x, y and z: 10 x 5 y z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

22 x z z y 5 x y 2. Cross-multiplying (y)(y)=(10)(5) y = |y|=7 y =7 and y=-7 5 y y 10 STANDARDS 4, 5, 14, 15 Find the value for x, y and z: = 5 y y 10 = x 5 y z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

23 x z y=7 5 x 2. z = z z = = z 2 |z|=12.2 z =12.2 and z=-12.2 STANDARDS 4, 5, 14, 15 Find the value for x, y and z: 10 x 5 y z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

24 x z y=7 5 x 2. z = x 22 2 x = = x 2 |x|=8.6 x=8.6 and x = -8.6 STANDARDS 4, 5, 14, 15 Find the value for x, y and z: 10 x 5 y z PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

25 x The length of a rectangle is 6 in and its width is 4 in. Find the length of its diagonal. 6 in 4 in = x 22 2 x = = x 2 x = 52 2 |x| = 7.2 x = 7.2 and x = STANDARDS 4, 5, 14, 15 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

26 z y x 4. STANDARDS 4, 5, 14, 15 Find the value for x, y and z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

27 z y x 4. z+22 z xx 22 y y 26 STANDARDS 4, 5, 14, 15 Find the value for x, y and z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

28 4. y z+22 z x x y 26 (26) z = (26)(26) 22 z STANDARDS 4, 5, 14, 15 Find the value for x, y and z: = z = z = z y x PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

29 4. y z+22 x y 26 xz= = x 22 2 x = = x 2 x = |x| =40.2 x= 40.2 and x =-40.2 STANDARDS 4, 5, 14, 15 Find the value for x, y and z: z y x PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

30 4. y z+22 yxx y 26 y = = y 2 |y|=34 y=34 and y = = y STANDARDS 4, 5, 14, 15 Find the value for x, y and z: z y x PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

31 5. z y x 16 9 STANDARDS 4, 5, 14, 15 Find the value for x, y and z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

32 z y x y y zz x x STANDARDS 4, 5, 14, 15 Find the value for x, y and z: PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

33 16 x 9 x = 5. y zz x 9 y x x = x 9 x |x|=12 x=12 and x=-12 Cross-multiplying (x)(x)=(16)(9) STANDARDS 4, 5, 14, 15 Find the value for x, y and z: = z y x 16 9 PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

34 5. y 16z z x=12 9 y z = = z 2 |z|=20 z =20 and z= = z STANDARDS 4, 5, 14, 15 Find the value for x, y and z: z y x PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

35 5. y 16 z z x=12 9 y y = = y = y |y|=15 y=15 and y=-15 STANDARDS 4, 5, 14, 15 Find the value for x, y and z: z y x PRESENTATION CREATED BY SIMON PEREZ. All rights reserved

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.