Proofs about Quadrilaterals
1) Lin is using the diagram to prove the statement, “If a parallelogram has one right angle, it is a rectangle.” Given that is a parallelogram and angle is right, which reasoning about angles will help her prove that angle is also a right angle?
2) is an isosceles trapezoid. Select all pairs of congruent triangles. Write each corresponding letter in the answer box and separate letters with commas.
a) Triangle and triangle b) Triangle and triangle c) Triangle and triangle d) Triangle and triangle e) Triangle and triangle
Match each conjecture with the rephrased statement of proof connected to the diagram.
Write the number of the corresponding statement in the answer box.
3) The diagonals of a parallelogram bisect each other.
4) In a parallelogram, opposite sides are congruent.
5) A quadrilateral with opposite sides congruent is a parallelogram.
6) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
7) Which of the following criteria always proves triangles congruent? Select all that apply. Write each corresponding letter in the answer box and separate letters with commas.
a) Corresponding congruent Angle-Side-Angle b) Corresponding congruent Side-Angle-Side c) Corresponding congruent Side-Side-Angle d) 3 congruent sides e) 2 congruent sides f) 3 congruent angles
8) Select all true statements based on the diagram. Write each corresponding letter in the answer box and separate letters with commas.
a) Segment is congruent to segment . b) Segment is congruent to segment . c) Segment is congruent to segment . d) Angle is congruent is angle . e) Angle is congruent to angle . f) Line is parallel to line . g) Line is parallel to line .
Diego states that diagonal bisects angles and .
9) Is he correct?
10) Explain your reasoning.
11) Sketch the unique triangles that can be made with angle measures and and side length 5.
12) How do you know you have sketched all possibilities?