Prove that opposite angles of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures.
1 answer:
<span>A parallelogram is a quadrilateral whose opposite sides are parallel. ABCD is a parallelogram; AB II CD and AC II BD
Theorem: </span><span>opposite angles of a parallelogram are congruent
Given: Parallelogram PQRS
Prove: </span>∠CAB = ∠BDC and ∠ABD= ∠DCA
Refer to the attached picture to follow.
Create an extended line beyond and name it as point E and point F.
Proof:
∠CDB = ∠EBD - alternate interior angle
∠EBD = ∠CAB - corresponding angle
This makes ∠CDB congruent to ∠CAB.
∠ACD = ∠FAC - alternate interior angle
∠FAC = ∠ABD - corresponding angle
This makes ∠ACD congruent to ∠ABD
Proving that ∠CAB = ∠BDC and ∠ABD= ∠DCA or ∠CAB = ∠CDB and ∠ABD = ∠ACD
Theorem: </span><span>opposite angles of a parallelogram are congruent
Given: Parallelogram PQRS
Prove: </span>∠CAB = ∠BDC and ∠ABD= ∠DCA
Refer to the attached picture to follow.
Create an extended line beyond and name it as point E and point F.
Proof:
∠CDB = ∠EBD - alternate interior angle
∠EBD = ∠CAB - corresponding angle
This makes ∠CDB congruent to ∠CAB.
∠ACD = ∠FAC - alternate interior angle
∠FAC = ∠ABD - corresponding angle
This makes ∠ACD congruent to ∠ABD
Proving that ∠CAB = ∠BDC and ∠ABD= ∠DCA or ∠CAB = ∠CDB and ∠ABD = ∠ACD
You might be interested in