MTH 503 Construction and Congruence

Which of the following statements most accurately describes congruent?

• Congruent means identical in form
• Congruent means completely different
• Congruent means partially similar
• Congruent means opposite

What is a perpendicular bisector?

• A line that cuts an object into two equal parts at a 60-degree angle

• A line that cuts an object into two equal parts at a 45-degree angle
• A line that cuts an object into two unequal parts at a 90-degree angle
• A line that cuts an object into two equal parts at a 90-degree angle

In the figure given below, BD is the bisector of ∠ABC and BE bisects ∠ABD. Find the measure of ∠DBE given that ∠ABC=80°.

(a)  

What bisects line AB at point O?

(a)  

State what additional information is required in order to know that the triangles are congruent for the reason given.

(a)  

Which of the following statements best describes PARALLEL LINES?

• Lines that intersect at a single point
• Lines that are always the same distance apart
• Lines that intersect at multiple points
• Lines that intersect at a 90 degree angle

In the figure, the ray drawn from point O is the angle bisector of ∠BON. Find the value of x.

• 5

• 4

• 3

• 2

Two triangles are congruent if and only if their corresponding sides and corresponding angles are congruent.
What criteria that states "If two triangles have two pairs of congruent angles and the common side of the angles (the side between the congruent angles) in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent?'

• SAS

• AAS

• ASA

• SSS

Lines p and q are intersected by line r, as shown in the diagram. If m<1 = 7x – 36 and m<2 = 5x + 12, for which the value of x that would make p||q.

(a)  

Complete the congruence statement for a pair of triangles.

(a)