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Refer to the figure below and tell whether each statement is true
publish date: 2023/05/12 20:32:00 GMT+10
- (1) ∠1 and ∠2 are congruent
- (2) ∠FGB and ∠CGE are congruent
- (3) ∠AGF and ∠FGE are congruent
- (4) ∠CGD and ∠CGB are congruent
- (5) ∠1 and ∠CGD are adjacent angles
- (6) ∠FGA and ∠AGC are supplementary
- (7) ∠AGB and ∠BGC are complementary
- (8) ∠AGF and ∠2 are complementary
Please drag and drop the selected option in the right place or type it instead
true
false
Correct Answer
(1) true
(2) true
(3) false
(4) false
(5) true
(6) true
(7) false
(8) true
Explanation
- ∠1 and ∠2 are congruent because they are vertical angles
- ∠FGB and ∠CGE are congruent because they are vertical angles
- ∠AGF and ∠FGE are not congruent because their measures are not the same, but they are adjacent and complementary angles
- ∠CGD and ∠CGB are not congruent because their measures are not the same, but they are adjacent and complementary angles
- ∠1 and ∠CGD are adjacent angles because they share the same vertex and side and they do not overlap
- ∠FGA and ∠AGC are supplementary because both make up a straight angle
- ∠AGB and ∠BGC are not complementary because both do not make up a right angle
- ∠AGF and ∠2 are complementary because both make up a right angle
Reference
Mathematics for college students