"If Two Straight Lines Are Parallel" Proof PPT Courseware 4

Description

"If Two Straight Lines Are Parallel" Proof PPT Courseware 4

learning target

(1) Understand the three properties of parallel lines.

(2) Be able to skillfully use these three properties to prove geometry problems.

(3) Further understand and summarize the steps, formats, and methods of proof.

(4) Understand the differences in conditions and structures between the two theorems, and experience the thinking process of forward and reverse.

collaborative inquiry

Draw the parallel line CD of the straight line AB, and think about the drawn parallel lines based on the drawing process. What is the relationship between the existing pair of co-position angles? Does every pair of homotopic angles have such a relationship?

Axiom: Two straight lines are parallel and have equal angles.

If two parallel lines are intercepted by a third straight line, their concentric angles are equal. So what is the relationship between interior angles and interior angles on the same side?

Prove: If two parallel straight lines are intercepted by a third straight line, their interior angles are equal.

It is known that: straight lines a∥b, ∠1 and ∠2 are the internal offset angles of straight lines a and b intercepted by straight line c.

Prove: ∠1=∠2.

Proof: ∵a∥b (known),

∴∠2=∠3 (two straight lines are parallel and have equal angles)

∵∠1=∠3 (the two vertex angles are equal),

∴∠1=∠2 (equivalent substitution)

Prove: If two parallel straight lines are intercepted by a third straight line, the interior angles on the same side are complementary.

It is known that: straight lines a∥b, ∠1 and ∠2 are interior angles on the same side intercepted by straight lines a and b by straight lines c.

Prove: ∠1+∠2=180°.

Proof: ∵a∥b (known)

∴∠2＝∠3 (two straight lines are parallel and have equal angles)

∵∠1+∠3 (1 straight angle=180°)

∴∠1+∠2=180 ° (equivalent substitution)

Classroom testing

1. It is known that parallel lines AB and CD are intercepted by straight line AE.

(1) From ∠1=110°, we can know what degree ∠2 is and why?

(2) From ∠1=110°, we can know what degree ∠3 is and why?

(3) From ∠1=110°, we can know what degree ∠4 is and why?

2. As shown in the figure, there is a part of a trapezoid with an upper base. Measure ∠A=115° and ∠D=100°. What are the degrees of each of the other two angles of the trapezoid?

3. As shown in the figure, it is known that straight line DE passes through point A, DE∥BC, ∠B=44°, ∠C=57°

(1) What degree is ∠DAB equal to?

(2) What degree is ∠EAC equal to?

According to the following propositions, draw the graph, and combine the graph to write the known and verified (do not write the proof process):

1) The distance from a point on the bisector of an angle to both sides of the angle is equal;

2) The bisectors of a pair of internal offset angles of two parallel lines are parallel to each other.

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Update Time: 2024-11-18

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