"Sum of Interior Angles Theorem of a Triangle" Proof of Parallel Lines PPT Download

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"Sum of Interior Angles Theorem of a Triangle" Proof of Parallel Lines PPT download, 12 pages in total.

Part One Content: Basic Knowledge Key Points

Knowledge point 1: Sum of interior angles of a triangle theorem

1. In △ABC, ∠A=∠B+∠C, then the correct judgment of the shape of △ABC is (A)

A. Right triangle B. Acute triangle

C. Obtuse triangle D. Equilateral triangle

2. As shown in the figure, it is known that in △ABC, ∠A=60°, ∠C=70°, points D and E are on AB and AC respectively, and DE∥BC. Then the degree of ∠ADE is (B)

A.40° B.50°

C.60° D.70°

3. It is known that the measure ratio of the three interior angles of a triangle is 2:3:4, then the measure of the largest angle in this triangle is 80°.

Sum of interior angles theorem of triangles PPT, part 2 content: improvement of comprehensive ability

7. (Textbook Motif Variation) As shown in the figure, AD and CE are the midline and angle bisector of △ABC respectively. If ∠B=∠ACB, ∠BAC=40°, then the degree of ∠ACE is (B)

A.20° B.35° C.40° D.70°

8. As shown in the figure, in △ABC, ∠C=70°. If ∠C is cut along the dotted line in the figure, then ∠1+∠2 is equal to (B)

A.360° B.250° C.180° D.140°

Sum of interior angles theorem of triangles PPT, the third part: Expanding exploration and breakthrough

14. Carefully read the following research fragment about the bisectors of the interior and exterior angles of a triangle and complete the questions raised.

Exploration 1: As shown in Figure 1, in △ABC, O is the intersection of the bisectors BO and CO of ∠ABC and ∠ACB. Through analysis, it is found that ∠BOC=90°+1/2∠A. Reason: ∵BO and CO respectively It is the bisector of ∠ABC and ∠ACB, ∴∠1=1/2∠ABC, ∠2=1/2∠ACB.

∴∠1+∠2=1/2( ∠ABC+∠ACB )=1/2( 180°-∠A )=90°-1/2∠A.

∴∠BOC=180°-( ∠1+∠2 )=180°-( 90°-1/2∠A )=90°+1/2∠A.

Research 2: As shown in Figure 2, O is the intersection point of BO and CO, the bisectors of ∠ABC and exterior angle ∠ACD. Try to analyze the relationship between ∠BOC and ∠A? Please explain the reason.

Keywords: Free download of Beijing Normal University edition eighth-grade mathematics PPT courseware for the first volume, PPT download of the sum of interior angles theorem of a triangle, PPT download of the proof of parallel lines, .PPT format;

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: 2024-12-08

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