Download Congruent triangles

Congruent triangles
Geometry
Geometric proof
1. In the diagram, PS = PQ and PR bisects QPS. Prove that RS = RQ.
P
Q
S
2.
R
In the diagram, AD is equal and parallel to CB. Prove that N is the midpoint of CD.
C
B
N
D
A
3. The diagram shows quadrilateral PQRS. Given that PQ = SR and that PS = QR, prove
that PQ is parallel to RS.
S
P
R
Q
Congruent triangles
Geometry
4. In the diagram, N is the foot of the perpendicular from P to line AB. If NAP = NBP,
prove that P is equidistant from A and B.
N
A
B
P
5. In the diagram below, A and B are the centres of the two circles, which meet at P and Q.
Prove that AB bisects PAQ.
P
A
B
Q
6. In the diagram below, M is the midpoint of AB and of CD. Prove that ACBD is a
parallelogram.
A
M
C
D
B
Congruent triangles
Geometry
7. In the diagram below, O is the centre of each of the circles. POQ and AOB are straight
lines. Prove AQ = PB.
A
Q
O
P
B
8. In the diagram below, line XYP is the bisector of both AXB and AYB. Prove that XY
is the perpendicular bisector of AB.
X
Y
A
B
P
9. In the diagram below, triangle AXB is congruent to triangle BYA. Prove that triangle AXY
is congruent to triangle BYX.
X
Y
A
B
10. If all four faces of a tetrahedron have the same perimeter then show that they are all
congruent.