Question

Just need someone to check my answers!! :)
Which statement is used to prove that angle ABD is congruent to angle ACD?

Angle CAB is congruent to angle CBA.
Angle DAC is congruent to angle DAB.
Triangle ACD is similar to triangle ABD.
**Segment AD is congruent to segment AC.

Answer 1

Which equation is true?
angle ABD = angle CDB
***angle DAB = angle DCB
angle DCB = angle ADB
angle ABD = angle BCD

Which pair of triangles is similar?
****Triangles PQR and QTS
Triangles QTS and SQR
Triangles PQR and RQS
Triangles QTS and SPR

Answer 2

Melissa writes the following proof for the theorem, “If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.”

Melissa’s proof

1. For triangles AOB and DOC, angle 1 is equal to angle 2 as they are vertical angles.
2. AO = OC and BO = OD because it is given that diagonals bisect each other.
3. The triangles AOB and DOC are congruent by SSS postulate.
4. Similarly, triangles AOD and BOC are congruent.
5. By CPCTC, AB is equal to DC.
6. By CPCTC, AD is equal to BC.
7. As the opposite sides are congruent the quadrilateral ABCD is a parallelogram.

Which is the first incorrect statement in Melissa’s proof?

Statement 3
Statement 4
Statement 5
****Statement 6