Tri-Form Quiz: Triangle Properties

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Triangle basics and formulas

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Yuleinis Urquiza pimienta

Colombia

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Tri-Form Quiz: Triangle PropertiesVersión en línea Triangle basics and formulas por Yuleinis Urquiza pimienta 1 Slide 1: Triangle Basics Triangles are polygons with three sides and three angles. The sum of interior angles is always 180 degrees. Classification by sides: equilateral, isosceles, scalene. 2 Slide 2: Side Classifications Equilateral: all sides equal. Isosceles: two sides equal. Scalene: all sides different. Equal sides imply equal angles opposite them. 3 Slide 3: Angle Sum Rule In any triangle, angle A + angle B + angle C = 180°. This rule helps determine missing angles and validate drawings. 4 Slide 4: Triangle Inequality For any triangle, the sum of any two sides is greater than the third: a + b > c etc. Prevents impossible triangles. 5 Slide 5: Pythagoras Theorem Right triangle: c² = a² + b², where c is hypotenuse. Useful for area and distance calculations. 6 Slide 6: Area Formulas Base-height: Area = ½ × base × height. Heron's formula: Area = √[s(s-a)(s-b)(s-c)] with semi-perimeter s. 7 Slide 7: Perimeter, Medians, and Altitudes Perimeter: sum of sides. Medians reach midpoints; centroid is their intersection. Altitude is perpendicular to the opposite side. 8 Slide 8: Centroid & Circumcenter Centroid: balancing point, divides medians 2:1. Circumcenter: equidistant from vertices, location varies by triangle type. 9 Slide 9: Triangle Similarity Similar triangles: corresponding angles equal. Criteria: AA, SSS, SAS. Proportional sides enable scale modeling. 10 Slide 10: Exterior Angles & Special Theorems Exterior angle equals sum of two remote interior angles. Use in proofs and problem solving to simplify calculations.

Tri-Form Quiz: Triangle PropertiesVersión en línea

Triangle basics and formulas

por Yuleinis Urquiza pimienta

Slide 1: Triangle Basics

Triangles are polygons with three sides and three angles. The sum of interior angles is always 180 degrees.

Classification by sides: equilateral, isosceles, scalene.

Slide 2: Side Classifications

Equilateral: all sides equal. Isosceles: two sides equal. Scalene: all sides different.

Equal sides imply equal angles opposite them.

Slide 3: Angle Sum Rule

In any triangle, angle A + angle B + angle C = 180°.

This rule helps determine missing angles and validate drawings.

Slide 4: Triangle Inequality

For any triangle, the sum of any two sides is greater than the third: a + b > c etc.

Prevents impossible triangles.

Slide 5: Pythagoras Theorem

Right triangle: c² = a² + b², where c is hypotenuse.

Useful for area and distance calculations.

Slide 6: Area Formulas

Base-height: Area = ½ × base × height.

Heron's formula: Area = √[s(s-a)(s-b)(s-c)] with semi-perimeter s.

Slide 7: Perimeter, Medians, and Altitudes

Perimeter: sum of sides. Medians reach midpoints; centroid is their intersection.

Altitude is perpendicular to the opposite side.

Slide 8: Centroid & Circumcenter

Centroid: balancing point, divides medians 2:1.

Circumcenter: equidistant from vertices, location varies by triangle type.

Slide 9: Triangle Similarity

Similar triangles: corresponding angles equal. Criteria: AA, SSS, SAS.

Proportional sides enable scale modeling.

Slide 10: Exterior Angles & Special Theorems

Exterior angle equals sum of two remote interior angles.

Use in proofs and problem solving to simplify calculations.

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