8 1 Similarity in Right Triangles
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This document discusses theorems and corollaries about right triangles. It states that if an altitude is drawn to the hypotenuse of a right triangle, the two triangles formed are similar. It also states that the length of the altitude is the geometric mean between the segments of the hypotenuse, and each leg is the geometric mean between the hypotenuse and adjacent hypotenuse segment. Students are assigned homework problems involving finding geometric means and values of unknowns in right triangles.
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The document discusses congruence and similarity in geometry. Congruence refers to two objects having the same shape and size. Similarity refers to two objects having the same shape, though not necessarily the same size. Specific examples are provided of congruent and similar line segments, angles, circles, polygons, and triangles. The concepts of uniform scaling, matching corresponding sides and angles, and proportional sides are also covered.
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This document discusses congruence and properties of congruent triangles. It defines congruence as two figures having the same size and shape, with corresponding angles and sides being congruent. If two triangles are congruent, corresponding angles and sides are congruent. The Third Angle Theorem states that if two angles of one triangle are congruent to two angles of another, the third angles are also congruent. Properties of congruent triangles include: reflexive, symmetric, and transitive properties. Examples are provided to illustrate these concepts.
Aparna assignment
1. The document discusses the concepts of natural resources, congruence, and similarity in geometry. It defines congruence as two figures having the same shape and size, and similarity as two figures having the same shape, whether in their normal or mirrored form.
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1) Congruent and similar triangles can be used to simplify design and calculations. Congruent triangles have equal sides and angles, while similar triangles have the same shape but not necessarily the same size.
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- 1. Chapter 8 Right Triangles 8-1 Similarity in Right Triangles
- 2. Geometric Mean If a, b, and x are positive numbers and 𝑎 𝑥 = 𝑥 𝑏 then x is called the geometric mean between a and b. Find the geometric mean between 22 and 55. 11 10
- 3. Simplifying Radicals • We will be leaving radicals in simplified radical form. • We will not be changing radicals to decimals. • Practice simplifying radicals and finding the geometric mean on the next slide and bring the answers to class tomorrow. (HW)
- 4. HW Part 1
- 5. Theorem 8-1 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. A BC N ∆𝐴𝐵𝐶~∆𝐴𝐶𝑁~∆𝐶𝐵𝑁
- 6. Corollary 1 When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse. A BC N 𝐴𝑁 𝐶𝑁 = 𝐶𝑁 𝐵𝑁
- 7. Corollary 2 When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. A BC N 𝐴𝐵 𝐴𝐶 = 𝐴𝐶 𝐴𝑁 and 𝐴𝐵 𝐵𝐶 = 𝐵𝐶 𝐵𝑁
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