Geometry, Parallel and Congruence Unit Test

What should be the next step to construct an equilateral triangle? (Be careful!)

• Construct segments AC and BC.

• Draw a circle centered at C with the radius AB.

• Draw segment AD and AC.

The rule (x,y)→(5x, 5y) maps △ABC to △A′B′C′. Which statement correctly describes the relationship between △ABC and △A′B′C′?

• The triangles are congruent because △A′B′C′ is a reflection of △ABC , and a reflection is a rigid motion.

• The triangles are congruent because △A′B′C′ is a rotation of △ABC, and a rotation is a rigid motion.

• The triangles are not congruent because △A′B′C′ is a reflection of △ABC, and a reflection is not a rigid motion.

• The triangles are not congruent because △A′B′C′ is a translation of △ABC, and a translation is not a rigid motion.

Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of alternate interior angles. What is a reasonable conjecture for Mei to make by recognizing a pattern and using inductive reasoning?

• When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.

• When a pair of parallel lines are intersected by a third line, all of the angles formed are congruent.

• When a pair of parallel lines are intersected by a third line, the alternate interior angles are acute.

• When a pair of parallel lines are intersected by a third line, all of the angles formed are obtuse.

Jamar draws three pairs of parallel lines that are each intersected by a third line. In each figure, he measures a pair of same-side interior angles. What is a reasonable conjecture for Jamar to make by recognizing a pattern and using inductive reasoning?

• When a pair of parallel lines are intersected by a third line, the same-side interior angles are acute.

• When a pair of parallel lines are intersected by a third line, all of the angles formed are supplementary.

• When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.

• When a pair of parallel lines are intersected by a third line, all of the angles formed are acute.

Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of vertical angles. What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning?

• When a pair of lines intersect, all of the angles formed are congruent.

• When a pair of lines intersect, the vertical angles are congruent.

• When a pair of lines intersect, the vertical angles are acute.

• When a pair of lines intersect, all of the angles formed are right angles.

It is given that E is the midpoint of DF . So, DE ≅(answer 1) by the definition of midpoint. Therefore, DE=EF by the (answer 2) DE+EF=DF by the (answer 3) and so DE+DE (answer 4) by substitution. Simplifying gives 2DE=DF.

• Segment Congruence Postulate

• Segment Addition Postulate

• E

• DF

Which statement is true about this argument? Premises: If a parallelogram has a right angle, then it is a rectangle. Parallelogram PQRSParallelogram PQRS has a right angle. Conclusion: Parallelogram PQRSParallelogram PQRS is a rectangle.

• The argument is valid by the law of syllogism.

• The argument is not valid because the conclusion does not follow from the premises.

• The argument is valid by the law of detachment.

• The argument is not valid because the premises are not true.

Match the following

• Transitive Property of Congruence

• 
• US=RS

• 
• RS = ST

• 
• Definition of an Isoceles Triangle

• 
• Given

• 

Jasmine draws three scalene triangles. In each figure, she measures each of the angles. What is a reasonable conjecture for Jasmine to make by recognizing a pattern and using inductive reasoning?

• In a scalene triangle, none of the angles are congruent.

• In a scalene triangle, all of the angles are acute.

• In a scalene triangle, none of the angles are right angles.

• In a scalene triangle, one of the angles is obtuse.

Which statement is true about this argument? Premises: If a triangle is an isosceles triangle, then it has two sides of equal length. If a triangle has two sides of equal length, then it has two angles of equal measure. Conclusion: If a triangle is an isosceles triangle, then it has two angles of equal measure.

• The argument is valid by the law of detachment.

• The argument is valid by the law of syllogism.

• The argument is not valid because the premises are not true.

• The argument is not valid because the conclusion does not follow from the premises.