Sudut Dalam dan Sudut Luar Segitiga (Matematika SMP kelas 7)

Innayatus Sholikhah
13 Apr 202013:10

Summary

TLDRIn this lesson, students explore the properties of triangles, focusing on the sum of interior and exterior angles. The teacher demonstrates how the sum of the interior angles of a triangle is always 180°, using various examples. The lesson also covers the relationship between exterior angles and the interior angles of a triangle, illustrating how the exterior angle equals the sum of the two non-adjacent interior angles. Several example problems are solved, including those involving angle sums and properties of isosceles triangles. The lesson concludes with a series of practice problems to reinforce the concepts.

Takeaways

  • 😀 The sum of the interior angles of a triangle is always 180°.
  • 😀 When the interior angles of a triangle are placed together, they form a straight angle (180°).
  • 😀 Example: If two angles in a triangle are 75° and 65°, the third angle can be found by subtracting their sum from 180° (40°).
  • 😀 The angles of a triangle can be in a ratio, such as 4:3:5, which allows you to find each angle using the equation 4A + 3A + 5A = 180°.
  • 😀 A triangle with angles 60°, 45°, and 75° is an acute triangle because all angles are less than 90°.
  • 😀 Exterior angles of a triangle are formed when one side is extended, and their relationship with interior angles is key.
  • 😀 The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
  • 😀 Example: In triangle ABC, extending side AB forms an exterior angle that is the sum of angles A and C.
  • 😀 Another exterior angle formed by extending side BC is the sum of angles B and C.
  • 😀 In triangle PQR, if it is an isosceles triangle, the base angles are equal. For example, if angle P equals angle R, their sum will help find the other angles.

Q & A

  • What is the sum of the interior angles of a triangle?

    -The sum of the interior angles of any triangle is always 180°.

  • How can we prove that the sum of the interior angles of a triangle is 180°?

    -We can prove it by placing the interior angles of a triangle (labeled as a, b, and c) on a straight angle (180°). By aligning the angles to form a straight line, we observe that the sum of the three angles equals 180°.

  • In the given example, how did they find the value of angle B?

    -In the example, it was given that two angles were 75° and 65°. The sum of these angles was subtracted from 180°, resulting in 40° for angle B.

  • What is the relationship between the angles in a triangle when the angles are in the ratio 4:3:5?

    -When the angles are in the ratio 4:3:5, we represent the angles as 4A, 3A, and 5A. Solving the equation 4A + 3A + 5A = 180° gives A = 15°. Therefore, the individual angles are 60°, 45°, and 75°.

  • What type of triangle is formed when all the interior angles are less than 90°?

    -When all the interior angles are less than 90°, the triangle is classified as an acute triangle.

  • What is the definition of an exterior angle of a triangle?

    -An exterior angle of a triangle is formed when a side of the triangle is extended. The angle formed outside the triangle is the exterior angle.

  • How do we find the value of an exterior angle based on the interior angles?

    -An exterior angle is equal to the sum of the two non-adjacent interior angles. For example, if angle A and angle C are inside the triangle, the exterior angle at vertex B is equal to A + C.

  • In the second exterior angle example, what relationship was used to find the exterior angle?

    -The relationship used was that the exterior angle at vertex B (angle CBD) is equal to the sum of the two opposite interior angles (angle A + angle C).

  • How can we calculate the interior angles of an isosceles triangle?

    -In an isosceles triangle, the two base angles are equal. For example, if the sum of these two angles is 112°, then each of the base angles is 56°.

  • How do you solve for an unknown angle in a triangle if the sum of two known angles is provided?

    -To solve for an unknown angle, subtract the sum of the known angles from 180°. For example, if the sum of two angles is 105°, then the unknown angle is 180° - 105° = 75°.

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Etiquetas Relacionadas
Triangle AnglesMath LessonGeometryAngles SumEducational ContentInterior AnglesExterior AnglesAngle Problem SolvingInteractive LearningStudent Engagement
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