"Sum of Interior Angle Theorem of a Triangle" Proof of Parallel Lines PPT Courseware 3

Description

"Sum of Interior Angle Theorem of a Triangle" Proof of Parallel Lines PPT Courseware 3

learning target

1. Understand the two corollaries and proofs of the sum of exterior angles and interior angles of a triangle theorem

2. Be able to use the two corollaries of the triangle interior angle sum theorem to solve related problems

Self-study guidance

1. Direct _______ from an axiom or theorem is called an inference of this axiom or theorem. The inference can be regarded as _______.

2. Corollary to the sum of interior angles theorem of a triangle:

An exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles

An exterior angle of a triangle is greater than any interior angle that is not adjacent to it

3. Exterior angle of a triangle: the angle formed by one side of the interior angle and the reverse extension of the other side.

4. A triangle has _______ exterior angles; the sum of each exterior angle and the adjacent interior angle is equal to _______; the sum of the interior angles of a triangle is equal to _______; the sum of the exterior angles of a triangle is equal to _______.

As shown in Figure 1: It is a five-pointed star. Verify: ∠A+∠B+∠C+∠D+∠E=180°

Solution: ∵∠1 is an exterior angle of △BDF (the meaning of exterior angle),

∴ ∠1=∠B+∠D (an exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles).

And ∵ ∠2 is an exterior angle of △EHC (the meaning of exterior angle),

∴ ∠2=∠C+∠E (an exterior angle of a triangle is equal to the sum of its two non-adjacent interior angles).

And ∵∠A+∠1+∠2=180° (triangle interior angle sum theorem).

∴ ∠A+∠B+∠C+∠D+∠E =180° (equality property)

Known: As shown in �ABC, AD⊥BC is in D, AE bisects ∠BAC (∠C>∠B),

Verify: ∠EAD=1/2(∠C-∠B)

Solution: ∵AE bisects ∠BAC,

∴∠BAE=∠CAE=1/2∠BAC

∵∠BAC=180°-(∠B+∠C)

∴∠EAC=1/2[180°-(∠B+∠C)]

∵AD⊥BC,

∴∠ADC=90°,

∴∠DAC=180°-∠ADC-∠C=90°-∠C,

∵∠EAD=∠EAC-∠DAC

∴∠EAD=1/2[180°-(∠B+∠C)]-(90°-∠C)=1/2(∠C-∠B)．

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For more information about the PPT courseware "Proof of Parallel Lines and the Sum of Interior Angle Theorem of Triangles", please click on the Proof of Parallel Lines PPT Theorem of Sum of Interior Angle of Triangles PPT tag.

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Update Time: 2024-09-08

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