Podcast
Questions and Answers
What is the sum of the interior angles of a triangle?
What is the sum of the interior angles of a triangle?
What type of angle is greater than 90°?
What type of angle is greater than 90°?
What is the condition for two triangles to be congruent using SSS?
What is the condition for two triangles to be congruent using SSS?
What is the condition for two triangles to be similar using AA?
What is the condition for two triangles to be similar using AA?
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What can be said about the lengths of two sides of a triangle compared to the length of the third side?
What can be said about the lengths of two sides of a triangle compared to the length of the third side?
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What is the condition for two triangles to be congruent using ASA?
What is the condition for two triangles to be congruent using ASA?
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What can be said about the exterior angles of a triangle?
What can be said about the exterior angles of a triangle?
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What type of triangle has three equal sides?
What type of triangle has three equal sides?
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What is the condition for two triangles to be similar using SSS?
What is the condition for two triangles to be similar using SSS?
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What is the condition for two triangles to be congruent using AAS?
What is the condition for two triangles to be congruent using AAS?
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Study Notes
Angles
- A triangle has three angles, which always add up to 180°.
- Angles can be classified as:
- Acute (less than 90°)
- Right (exactly 90°)
- Obtuse (greater than 90°)
- Straight (exactly 180°)
- The sum of the interior angles of a triangle is always 180°.
- Exterior angles of a triangle are equal to the sum of the two non-adjacent interior angles.
Sides
- A triangle has three sides, which can be classified as:
- Equal (in an equilateral triangle)
- Unequal (in a scalene triangle)
- Two equal sides (in an isosceles triangle)
- The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
- The length of the third side is always less than the sum of the lengths of the other two sides.
Congruence
- Two triangles are congruent if they have the same shape and size.
- Congruence can be determined by:
- SSS (side-side-side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
- SAS (side-angle-side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
- ASA (angle-side-angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
- AAS (angle-angle-side): If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.
Similarities
- Two triangles are similar if they have the same shape but not necessarily the same size.
- Similarity can be determined by:
- AA (angle-angle): If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
- SSS (side-side-side): If the ratios of corresponding sides of two triangles are equal, the triangles are similar.
- SAS (side-angle-side): If the ratios of two sides and the included angle of one triangle are equal to the ratios of two sides and the included angle of another triangle, the triangles are similar.
Trigonometry
- Trigonometry is the study of the relationships between the sides and angles of triangles.
- Important trigonometric concepts include:
- Sine (sin): Opposite side / Hypotenuse
- Cosine (cos): Adjacent side / Hypotenuse
- Tangent (tan): Opposite side / Adjacent side
- Pythagorean identity: sin^2(A) + cos^2(A) = 1
- Trigonometric identities: sin(A+B) = sin(A)cos(B) + cos(A)sin(B), etc.
Angles
- A triangle has three angles, which always add up to 180°.
- Angles can be classified as acute (less than 90°), right (exactly 90°), obtuse (greater than 90°), or straight (exactly 180°).
- The sum of the interior angles of a triangle is always 180°.
- Exterior angles of a triangle are equal to the sum of the two non-adjacent interior angles.
Sides
- A triangle has three sides, which can be classified as equal (in an equilateral triangle), unequal (in a scalene triangle), or two equal sides (in an isosceles triangle).
- The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
- The length of the third side is always less than the sum of the lengths of the other two sides.
Congruence
- Two triangles are congruent if they have the same shape and size.
- Congruence can be determined by:
- SSS (side-side-side): If three sides of one triangle are equal to three sides of another triangle.
- SAS (side-angle-side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
- ASA (angle-side-angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
- AAS (angle-angle-side): If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.
Similarities
- Two triangles are similar if they have the same shape but not necessarily the same size.
- Similarity can be determined by:
- AA (angle-angle): If two angles of one triangle are equal to two angles of another triangle.
- SSS (side-side-side): If the ratios of corresponding sides of two triangles are equal.
- SAS (side-angle-side): If the ratios of two sides and the included angle of one triangle are equal to the ratios of two sides and the included angle of another triangle.
Trigonometry
- Trigonometry is the study of the relationships between the sides and angles of triangles.
- Important trigonometric concepts include:
- Sine (sin): Opposite side / Hypotenuse.
- Cosine (cos): Adjacent side / Hypotenuse.
- Tangent (tan): Opposite side / Adjacent side.
- Pythagorean identity: sin^2(A) + cos^2(A) = 1.
- Trigonometric identities: sin(A+B) = sin(A)cos(B) + cos(A)sin(B), etc.
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Description
Learn about the properties of triangles, including angles, sides, and their classifications. Understand how to identify and work with different types of angles and sides in triangles.
