Buzz
With the study material for Grade 7 math problems on page 108 Volume 1 Canh Dieu Book providing detailed solutions for exercises in Lesson Review Chapter IV, students can easily refer to and solve every exercise, as well as reinforce the knowledge learned in Chapter IV.
Refer to various study materials for Grade 7 Math
- Solving Grade 7 Math Volume 1 Canh Dieu Book
- Solving Grade 7 Math on page 87 Volume 1 Connect Knowledge Book - End-of-chapter exercises 4
- Solving Grade 7 Math on page 86, 87 Volume 1 Creative Horizon Book - End-of-chapter exercises 4
Grade 7 math problems on page 108 Volume 1 Canh Dieu Book
Chapter IV Review Exercises
1. Solve Exercise 1 on Page 108 Math Grade 7 Textbook
Question: a) Provide an example of two adjacent angles, two supplementary angles, two vertical angles.
b) What is the definition of an angle bisector?
Give an example of two congruent angles, and two supplementary angles.
If a line intersects two parallel lines, are the corresponding angles congruent? Are the alternate interior angles congruent?
State Euclid's postulate about parallel lines.
Solution:
Two vertical angles are two angles where each side of one angle forms a straight line with a side of the other angle.
Two angles with a common vertex and one common side, where the other two sides lie on opposite sides of the line containing the common side, are called adjacent angles.
Two angles whose measures sum up to 180 degrees are called supplementary angles.
Two adjacent angles are supplementary if they are adjacent and their measures add up to 180 degrees.
The angle bisector of an angle is a ray within the angle that divides the angle into two equal angles.
A line intersecting two parallel lines produces pairs of corresponding angles equal to each other and pairs of alternate interior angles equal to each other.
Euclid's postulate about parallel lines.
Answer:
a)
The angle xOy and the angle yOz in the figure below are adjacent angles.
The angle mOp and the angle pOn are adjacent supplementary angles.
The angle A1 and the angle A3 are vertical angles.
b) The angle bisector of an angle is a ray within the angle that divides the angle into two equal angles.
c)
When line c intersects lines a and b, it forms: Angle A1 and B1 are corresponding angles; Angle A2 and B1 are alternate interior angles.
d) If a line intersects two parallel lines, then the corresponding angles are equal; the alternate interior angles are equal (Property of parallel lines).
e) Euclid's postulate on parallel lines: Through a point outside a given line, there exists one and only one line parallel to the given line.
2. Solve Exercise 2 on Page 108 of Mathematics Textbook Grade 7
Problem: a) Do two angles with measures totaling 180o constitute a pair of supplementary angles?
b) Are two angles equal in measure and sharing a vertex necessarily vertical angles?
Solution:
Provide an example disproving the statement.
Answer:
a) Two angles with measures totaling 180o are not necessarily supplementary angles, because supplementary angles must be adjacent and have a total measure of 180o, for example:
Angle xOy and angle xOz have a total measure of 180o but are not adjacent angles, as they are not adjacent.
b) Two angles equal in measure and sharing a vertex are not necessarily vertical angles, for example:
Angle mAq and angle nAp are equal in measure and share a vertex, but are not vertical angles.
3. Solve Exercise 3 on Page 108 of Mathematics Textbook Grade 7
Problem: Find pairs of parallel lines in each of the figures 53a, 53b, 53c, 53d and explain why?
Solution:
+ Use the criterion for recognizing parallel lines: If a line intersects two other lines creating either a pair of alternate interior angles or a pair of corresponding angles that are congruent, then those two lines are parallel.
+ Two adjacent supplementary angles have a total measure of 180 degrees.
Answer:
a)
c)
d)
4. Solve Exercise 4 on Page 108 of Mathematics Textbook Grade 7
Solution:
+ Two lines parallel to a third line are parallel to each other.
+ Use the property of parallel lines: If a line intersects two parallel lines, then the pairs of alternate interior angles are congruent, and the pairs of corresponding angles are congruent.
Answer:
a) Because AE ⊥ AB; AE ⊥ ED so AB // ED (Two lines perpendicular to a third line are parallel to each other).
Given that Cx // AB (given)
⇒ Cx // ED (Two lines parallel to a third line are parallel to each other).
5. Solve Exercise 5 on Page 108 of Mathematics Textbook Grade 7
Problem: Observe Figure 55, where mq // xt.
a) Name the pairs of corresponding angles.
b) Find the measures of angle BAC and angle CDE.
Solution:
+ Two lines parallel to a third line are parallel to each other.
+ Use the property of parallel lines: If a line intersects two parallel lines, then the pairs of alternate interior angles are congruent, and the pairs of corresponding angles are congruent.
Answer:
a) The pairs of corresponding angles are: angle mAn and angle xEn; angle mAz and angle xEz; angle nAq and angle nEt; angle qAz and angle tEz; angle pBq and angle pDt; angle qBy and angle tDy; angle mBy and angle xDy; angle pBm and angle pDx.
c)
Nam's statement is correct because:
