Similarity in Right Triangles Right Triangle Relationships Theorem

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Similarity in Right Triangles

Similarity in Right Triangles

Right Triangle Relationships Theorem 7 -3: The altitude to the hypotenuse of a right

Right Triangle Relationships Theorem 7 -3: 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.

Identifying Similar Triangles • What similarity statement can you write relating the three triangles

Identifying Similar Triangles • What similarity statement can you write relating the three triangles in the diagram?

What similarity statement can you write relating the three triangles in the diagram

What similarity statement can you write relating the three triangles in the diagram if the “big” triangle is QRP?

Geometric Mean • For any two positive integers a and b, the geometric mean

Geometric Mean • For any two positive integers a and b, the geometric mean of a and b is the positive number x such that.

Finding geometric means Find the geometric mean of each pair of numbers. If necessary,

Finding geometric means Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 4 and 25

Finding geometric means Find the geometric mean of each pair of numbers. If necessary,

Finding geometric means Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 5 and 30

Geometric Means in Right Triangles Corollary 1: The length of the altitude to the

Geometric Means in Right Triangles Corollary 1: 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.

Geometric Means in Right Triangles Corollary 2: The altitude to the hypotenuse of a

Geometric Means in Right Triangles Corollary 2: 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 hypotenuse and the length of the segment of the hypotenuse adjacent to the leg.

Using the Corollaries • What are the values of x and y?

Using the Corollaries • What are the values of x and y?

What are the values of x and y?

What are the values of x and y?

Finding a Distance • You are preparing for a robotics competition using the setup

Finding a Distance • You are preparing for a robotics competition using the setup shown. You program the robot to move from A to D and pick up the plastic bottle. How far does the robot travel from A to D?

SIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity TheoremSIMILARITY THEOREMS Similarity in Triangles AngleAngle Similarity Theorem
Special Right Triangles Theorem 4590 Triangle Theorem InSpecial Right Triangles Theorem 4590 Triangle Theorem In
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
Right Triangles Right Triangles n A triangle withRight Triangles Right Triangles n A triangle with
SIMILARITY 9 5 Right Triangles and Similar TrianglesSIMILARITY 9 5 Right Triangles and Similar Triangles
Triangles Triangles classified by their angles Right triangleTriangles Triangles classified by their angles Right triangle
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