Refer to the diagram and name each of the following.
Problem 1 :
An angle adjacent to ∠PQT _____
Solution :
Adjacent angle :
Two angles are adjacent if they have a common vertex and a common side.
In the diagram, the two angles PQT and TQR are adjacent.
Problem 2 :
The ray opposite to the ray TS _____
Solution :
Opposite rays :
Two rays are opposite rays, by definition, if
1) They have the same endpoint, and
2) Their union is a line.
In the diagram, opposite ray is QR or PR.
Problem 3 :
An obtuse angle _____
Solution :
An angle that is greater than 90^{º} and less than 180^{º} is called obtuse angle.
Problem 4 :
The sides of ∠TQR ____ and _____
Solution :
So, the sides is ∠TQP are TQ and QR.
Problem 5 :
Two right angles _____ and ____
Solution :
Two right angles measures is 90^{º} and 90^{º}
So, two right triangle is ∠PTQ and ∠STQ
Problem 6 :
A point on the line PQ that is not on line segment PQ _____
Solution :
R is the point of PQ which is not in the line segment PQ.
Problem 7 :
The vertex of the 20^{º} angle _____
Solution :
The vertex of the 20^{º} angle is P.
Problem 8 :
The point between P and R _____
Solution :
The point between P and R is Q.
Classify each statement as true or false.
Problem 1 :
Through any two points there is exactly one line. _____
Solution :
Yes, it is true. Because exactly one line to pass through two points.
Problem 2 :
Through any three points there is exactly one line. _____
Solution :
Yes, it is true. A line can be drawn by connecting infinite points, so any three points can be on the line.
Problem 3 :
Through any three points there is exactly one plane. _____
Solution :
It is false. Because through any three non - collinear points, there exists exactly one plane.
Problem 4 :
Two lines intersect in exactly one point. _____
Solution :
Yes, it is true.
Problem 5 :
Two planes intersect in exactly one point. _____
Solution :
It is false. Because planes are infinite.
Problem 6 :
Two planes intersect in a line. _____
Solution :
Yes it is true. If two planes intersect, then their intersection is a line.
Problem 7 :
A line and a plane can intersect in a point. _____
Solution :
A line and plane can intersect at a point, sometime infinitely many points.
So, it is true.
Complete each statement with the word always, sometimes, or never.
Problem 1 :
Adjacent angles are _____ congruent.
Solution :
Adjacent angles are sometimes congruent. The equivalent angle measure would be 90 degree.
Adjacent angles are angles that come out of the same vertex.
Problem 2 :
If points A and B are in plane R and point C is on AB, then C is _____ in R.
Solution :
If points A and B are in plane R and point C is on AB, then C is always in R.
Problem 3 :
Two intersecting lines _____ lie in exactly one plane.
Solution :
Two intersecting lines always lie in exactly one plane.
Problem 4 :
A line and a point not on the line _____ lie in more than one plane.
Solution :
A line and a point not on the line never lie in more than one plane.
Problem 5 :
A line _____ contains at least two points.
Solution :
A line always contains at least two points.
Jun 05, 23 09:20 PM
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