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"Perpendicular Lines" Intersecting Lines and Parallel Lines PPT Courseware 2
Question: How many perpendicular lines to l can be drawn through the known straight line l and a point A on (or outside) l?
You can make one, and only one.
in conclusion:
There is only one straight line through a point that is perpendicular to the known straight line.
Notice:
Drawing a perpendicular to a known line segment (or ray) through a point is the perpendicular to the straight line where this line segment (or ray) is located.
Consolidation exercises
Multiple choice questions
1. Of the following four methods of judging that two straight lines are perpendicular, ___ are correct [ ]
(1) If one of the four angles formed by the intersection of two straight lines is a right angle, then the two straight lines are perpendicular to each other.
(2) If two straight lines intersect and have a set of adjacent supplementary angles that are equal, then the two straight lines are perpendicular to each other.
(3) When two straight lines intersect, the four angles they form are equal. The two straight lines are perpendicular to each other.
(4) If two straight lines intersect and have a set of complementary vertex angles, then the two straight lines are perpendicular to each other.
A. 4B. 3C. 2D. 1
2. Among the four angles formed by the intersection of two straight lines, which of the following conditions can determine whether the two straight lines are perpendicular to [ ]
A. There are two equal angles B. There are two pairs of angles that are equal
C. There are three equal angles D. There are four pairs of adjacent supplementary angles
3． The bisectors of two angles are perpendicular to each other: [ ]
A. The two angles are complementary; B. The two angles are opposite angles to each other;
C. Both angles are right angles; D. Two angles are adjacent supplementary angles
Of all the line segments connecting a point outside the straight line to every point on the straight line, the perpendicular segment is the shortest.
Simply put: the vertical line segment is the shortest.
The length from a point outside a straight line to the perpendicular segment of the straight line is called the distance from the point to the straight line.
Can you design?
Question 1: There is an ant at vertex A of the cuboid that wants to climb to point C. Please help it draw the best route for crawling. and explain the reasons.
Question 2: If the ant at A wants to climb to edge BC, what do you think is its best route?
Question 3: If the ant is at point M and wants to climb to edge BC, please design an optimal route.
think
1. Which of the three sides of a right triangle is the longest?
Answer: The side opposite to a right angle is the longest.
2. As shown in the figure, AC⊥BC, ∠C=900, the shortest line segment AC, BC, CD is ( )
(A) AC (B) BC (C) CD (D) Unsure
summary
Recall the knowledge about the intersection of two straight lines and ask: Can you draw them into a knowledge structure diagram?
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