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Questions and Answers
Given two similar triangles ABC and DEF, if the sides of ABC are 3, 4, and 5 units, and the corresponding sides of DEF are 9, 12, and 15 units, what is the scale factor relating the two triangles?
Given two similar triangles ABC and DEF, if the sides of ABC are 3, 4, and 5 units, and the corresponding sides of DEF are 9, 12, and 15 units, what is the scale factor relating the two triangles?
In a right triangle ABC with hypotenuse c, if the altitude from A to the hypotenuse divides the hypotenuse into segments of lengths $x$ and $y$, which of the following statements is true?
In a right triangle ABC with hypotenuse c, if the altitude from A to the hypotenuse divides the hypotenuse into segments of lengths $x$ and $y$, which of the following statements is true?
In a 45-45-90 right triangle with legs of length $l$ and hypotenuse of length $h$, which of the following statements is true?
In a 45-45-90 right triangle with legs of length $l$ and hypotenuse of length $h$, which of the following statements is true?
If two similar polygons have a scale factor of $k$, what is the ratio of their perimeters?
If two similar polygons have a scale factor of $k$, what is the ratio of their perimeters?
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Which of the following statements is true about the Sierpinski triangle?
Which of the following statements is true about the Sierpinski triangle?
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Which of the following is a statement that needs to be proven before being accepted?
Which of the following is a statement that needs to be proven before being accepted?
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Two angles whose sum is the measure of 90° are called what?
Two angles whose sum is the measure of 90° are called what?
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A quadrilateral with exactly one pair of opposite sides parallel is called a:
A quadrilateral with exactly one pair of opposite sides parallel is called a:
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If two polygons have congruent corresponding angles and proportional corresponding sides, they are called:
If two polygons have congruent corresponding angles and proportional corresponding sides, they are called:
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The AAA Similarity Postulate states that if the $three$ angles of one triangle are congruent to the $three$ angles of another triangle, then the two triangles are:
The AAA Similarity Postulate states that if the $three$ angles of one triangle are congruent to the $three$ angles of another triangle, then the two triangles are:
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Study Notes
Similar Triangles
- The scale factor relating two similar triangles is the ratio of the lengths of corresponding sides.
- In the given example of triangles ABC and DEF, the scale factor is 3 because the sides of DEF are 3 times larger than the corresponding sides of ABC.
Right Triangle Properties
- In a right triangle, the altitude from the right angle to the hypotenuse divides the triangle into two smaller similar right triangles.
- The altitude is the geometric mean of the two segments of the hypotenuse.
45-45-90 Right Triangles
- In a 45-45-90 right triangle, the legs are congruent and the hypotenuse is $\sqrt{2}$ times the length of each leg.
Similar Polygons
- The ratio of the perimeters of two similar polygons is equal to the scale factor.
Sierpinski Triangle
- The Sierpinski triangle is a fractal.
- It is created by repeatedly removing the middle triangle from an equilateral triangle.
Geometric Statements
- A statement that needs to be proven before being accepted is called a conjecture.
Angle Pairs
- Two angles whose sum is 90° are called complementary angles.
Quadrilaterals
- A quadrilateral with exactly one pair of opposite sides parallel is called a trapezoid.
Similarity
- If two polygons have congruent corresponding angles and proportional corresponding sides, they are called similar polygons.
AAA Similarity Postulate
- The AAA Similarity Postulate states that if the three angles of one triangle are congruent to the three angles of another triangle, then the two triangles are similar.
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Description
Test your knowledge of mathematical terms with this quiz covering definitions like theorem, adjacent angles, base angles, complementary angles, and more. See how well you understand key concepts in geometry and trigonometry.
