geometry a - unit 4: exam

use the diagram and information to complete the proof. given: △tvw ≅△vtu prove: quadrilateral tuvw is a parallelogram. match each numbered statement in the proof with the correct reason.

1. given 2. corresponding parts of congruent triangles are congruent. 3. angle addition postulate 4. substitution property of equality 5. if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

use the following diagram and information to complete the proof. given: lmno is a parallelogram. △lpo ≅△opn prove: lmno is a rhombus. match each numbered statement to the correct reason to complete the proof.

1. given 2. corresponding parts of congruent triangles are congruent. 3. opposite sides of parallelograms are congruent. 4. substitution property of congruence 5. definition of rhombus

match each numbered statement for steps 3 through 7 with the correct reason.

3. opposite sides of a parallelogram are congruent 4. XXX corresponding parts of congruent triangles are congruent 5. reflective property of congruence 6. XXX right angle theorem 7. XXX sas congruence theorem

examine parallelogram abcd. if m∠a = (3x) and m∠d = (x + 60), what value of x makes abcd a parallelogram? enter the correct value of x.

30

what is the measure of rs?

5

what is the length of ab?

56

if △abc ≅△ade, what is the length of ae?

7

which answer correctly describes how to prove quadrilateral qrst is a parallelogram?

XXX show that ∠tqs ≅∠rst by the alternate interior angles theorem. then, with the reflexive property of congruence and aas congruence theorem, show that △tqs ≅△rst. since qt∥rs, qr ≅ st and qt ≅ rs, so qrst is a parallelogram by definition. XXX show that ∠tqs ≅∠rst by the alternate interior angles theorem. then, with the reflexive property of congruence and aas congruence theorem, show that △tqs ≅ △rst. since corresponding parts of congruent triangles are congruent, qr≅st and qt≅rs, so qrst is a parallelogram by definition.

which plan should you use to prove that an angle of abcd is supplementary to both of its consecutive angles?

XXX use m∠a = 104 and m∠b = 76 to show that ∠a and ∠b are supplementary angles by the same-side interior angles theorem. then, use ab∥cd to show that ∠a and ∠d are supplementary. XXX use ab∥cd to show that ∠a and ∠c are same-side interior angles by the same-side interior angles theorem. then, use m∠a = 104∘ and m∠b = 76∘ to show that ∠a and ∠b are supplementary angles.

match each blank with the option that correctly fills in that blank in the proof.

blank 1 (reason 4) : reflexive property of congruence blank 2 (statement 5) : cda

if gerrard knows that △wxv ≅ △uxt, how can gerrard prove that quadrilateral tuvw is a parallelogram?

gerrard can show that wx ≅ ux and tx ≅ vx because corresponding parts of congruent triangles are congruent. from that he can conclude that s is the midpoint of tv and uw so tv and uw bisect each other. thus, quadrilateral tuvw is a parallelogram.

julie wants to prove that abcd is a square. she uses properties of congruent triangles and parallelograms to prove that ∠a ≅∠b ≅∠c ≅∠d. she must also show that ab ≅ bc ≅ cd ≅ da to prove abcd is a square. what else must Julie do to prove abcd is a square?

julie can use properties of congruent triangles to show that ab≅bc and bc≅cd. then she can show bc≅ad because opposite sides of a parallelogram are congruent.

which statement must be true to be able to use the aas congruence theorem to prove △lmn ≅ △pon?

n is the midpoint of lp

is it possible to prove that the triangles are congruent by using the aas congruence theorem?

no, possible to prove that the triangles are congruent by using the aas congruence theorem?

which of the following statements can be used to prove quadrilateral qrst is a parallelogram?

qr ≅ st and qt ≅ rs

cassius knows that ae ≅ ce and be ≅ de. how can cassius prove that quadrilateral abcd is a parallelogram?

since ae ≅ ce and be ≅ de then e is the midpoint of ac and bd. cassius can use that to show that ac and bd bisect each other, and thus quadrilateral abcd is a parallelogram.

which answer correctly fills in the blank for step 3?

since consecutive angles in a parallelogram are supplementary, m∠bad +m∠cda = 180∘.

which answer correctly fills in the blank for statement 8 of the proof to show that the diagonals of wxyz bisect each other?

v V is the midpoint of xz and wy

abraham proved that consecutive angles in the parallelogram are supplementary. he first used same-side interior angles by using a diagonal. then he used the same-side interior angles theorem. which pairs of angles could he have used with the same-side interior angles theorem?

∠a and ∠d, ∠b and ∠c

which statement about △uvw and △xyz is true?

△uvw ≅△xyz by the hl congruence theorem.