"Interior Angle of a Triangle" Triangle PPT Courseware

Description

"Interior Angle of a Triangle" Triangle PPT Courseware

The sum of the interior angles of a triangle is 1800.

Proof method one

Extend BC to D, outside △ABC, with CA as one side,

Outside △ABC, with CA as one side,

Therefore CE∥BA (the internal offset angles are equal and the two straight lines are parallel).

∴∠B=∠2 (the two straight lines are parallel and have equal angles).

∵∠1+∠2+∠ACB=180°

∴∠A+∠B+∠ACB=180°

Proof method two

Extend BC to D, cross C and make CE∥BA,

∴ ∠A=∠1 (the two straight lines are parallel and the internal offset angles are equal)

∠B=∠2 (two straight lines are parallel and have equal angles)

∵∠1+∠2+∠ACB=180°

∴∠A+∠B+∠ACB=180°

summary

1. The sum of the interior angles of a triangle: the sum of the three interior angles of a triangle is 180°

2. From the sum of the interior angles of a triangle equal to 180°, it can be concluded that

(1) The two acute angles of a right triangle are mutually complementary;

(2) A triangle has at most one right or obtuse angle;

(3) In any triangle, there are at most three acute angles and at least two acute angles;

(4) At least one angle in a triangle is less than or equal to 60°

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Update Time: 2024-09-09

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 1 industry PPT template

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