Similarity in Right Triangles Geometry 8 4 Supplies

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Similarity in Right Triangles Geometry 8 -4

Similarity in Right Triangles Geometry 8 -4

• Supplies • One sheet of computer paper • Scissors Exploration

• Supplies • One sheet of computer paper • Scissors Exploration

• Cut a sheet of paper into a rectangle (fold to create a

• Cut a sheet of paper into a rectangle (fold to create a perfect rectangle) • Don’t be lazy and use the whole sheet of paper Exploration

• Draw a diagonal on the paper, and cut Exploration

• Draw a diagonal on the paper, and cut Exploration

• Fold and cut along the altitude of one triangle Exploration

• Fold and cut along the altitude of one triangle Exploration

• Label the angles as shown 5 7 2 4 6 8 9

• Label the angles as shown 5 7 2 4 6 8 9 1 Exploration 3

• Compare the angles on the three triangles 5 7 2 4 6

• Compare the angles on the three triangles 5 7 2 4 6 8 9 1 Exploration 3

• Which angles are congruent to angle 1? 4 and 7 • Which

• Which angles are congruent to angle 1? 4 and 7 • Which angles are congruent to angle 2? 6 and 8 • Which angles are congruent to angle 3? 5 5 and 9 7 2 4 6 8 9 1 Exploration 3

• So. . . What is true about all three triangles? They are

• So. . . What is true about all three triangles? They are similar 5 7 2 4 6 8 9 1 Exploration 3

• Write a similarity statement C A D Exploration B

• Write a similarity statement C A D Exploration B

• Geometric Mean – A proportion with the same variable in each fraction

• Geometric Mean – A proportion with the same variable in each fraction as shown Geometric Means

Example

Example

Theorem and corollaries

Theorem and corollaries

Theorem and corollaries

Theorem and corollaries

Example

Example

Example

Example

Example

Example

Example

Example

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

• Pages 442 – 444 • 15, 18, 30 – 36 even, 42,

• Pages 442 – 444 • 15, 18, 30 – 36 even, 42, 44, 50, 52, 62 64 Homework

• Pages 442 – 444 • 15, 18, 30 – 36 even, 39,

• Pages 442 – 444 • 15, 18, 30 – 36 even, 39, 42, 44, 50, 52, 62 - 64 Honors Homework

SIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity PostulateSIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity Postulate
SIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity PostulateSIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity Postulate
SIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity TheoremSIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity Theorem
SIMILARITY 9 5 Right Triangles and Similar TrianglesSIMILARITY 9 5 Right Triangles and Similar Triangles
Similarity in Right Triangles Right Triangle Relationships TheoremSimilarity in Right Triangles Right Triangle Relationships Theorem
LESSON EIGHTEEN SPECIAL RIGHT TRIANGLES SPECIAL RIGHT TRIANGLESLESSON EIGHTEEN SPECIAL RIGHT TRIANGLES SPECIAL RIGHT TRIANGLES
Right Triangles Right Triangles n A triangle withRight Triangles Right Triangles n A triangle with
45 45 90 right triangles Some right triangles45 45 90 right triangles Some right triangles
45 45 90 right triangles Some right triangles45 45 90 right triangles Some right triangles
Special Right Triangles What are Special Right TrianglesSpecial Right Triangles What are Special Right Triangles
Distance Similarity Measures Similarity and Dissimilarity Similarity NumericalDistance Similarity Measures Similarity and Dissimilarity Similarity Numerical
Similarity Proportions Similarity Statements Similarity Ratio 10 10Similarity Proportions Similarity Statements Similarity Ratio 10 10
NLP Text Similarity Morphological Similarity Stemming Morphological SimilarityNLP Text Similarity Morphological Similarity Stemming Morphological Similarity
Similarity Similarity Similar Not Similar Similar triangles 1Similarity Similarity Similar Not Similar Similar triangles 1
Special Right Triangles Geometry 7 3 Special RightSpecial Right Triangles Geometry 7 3 Special Right
Geometry Unit 5 Jeopardy Special right Triangles RightGeometry Unit 5 Jeopardy Special right Triangles Right
Projective Geometry Projective Geometry Projective Geometry Projective GeometryProjective Geometry Projective Geometry Projective Geometry Projective Geometry
Similar Triangles Identify Similar Triangles Triangles are similarSimilar Triangles Identify Similar Triangles Triangles are similar
SIMILAR TRIANGLES Identify similar triangles Use similar trianglesSIMILAR TRIANGLES Identify similar triangles Use similar triangles
Lesson 4 3 Congruent Triangles Congruent triangles trianglesLesson 4 3 Congruent Triangles Congruent triangles triangles
Similar Triangles When are triangles considered similar TrianglesSimilar Triangles When are triangles considered similar Triangles
Inequalities in Triangles Inequalities in Triangles Triangles haveInequalities in Triangles Inequalities in Triangles Triangles have
4 3 Congruent Triangles Congruent triangles Triangles that4 3 Congruent Triangles Congruent triangles Triangles that
Advanced Geometry Similarity Lesson 2 Proportions Similarity RatioAdvanced Geometry Similarity Lesson 2 Proportions Similarity Ratio