Congruence of triangles:
Two triangles are said to be congruent if
all three corresponding sides are equal
and all the three corresponding angles are
equal in measure. These triangles can be
slides, rotated, flipped and turned to be
looked identical.
•Congruence of Triangles Rules
•The different criteria used to prove congruency
between two triangles are:
•SSS Criteria: Side-Side-Side
•SAS Criteria: Side-Angle-Side
•ASA Criteria: Angle-Side-Angle
•AAS Criteria: Angle-Angle-Side
•RHS Criteria: Right angle- Hypotenuse-Side
Q. AB is a line segment and P is its mid-point. D and E are
points on the same side of AB such that BAD = ABE and
EPA = DPB (see the above right sided figure). Show that
(i)DAP EBP (ii) AD = BE
Q. In the figure PQRS is a quadrilateral and T and U
are respectively points on PS and RS such that PQ =
RQ, PQT = RQU and TQS = UQS. Prove that
QT = QU.
Q. ABC is an isosceles triangle in which AB = AC.
Side BA is produced to D such that AD = AB (see the
above right sided figure). Show that BCD is a right
angle.
Q. AB is a line-segment. P and Q are points on opposite sides
of AB such that each of them is equidistant from the points A
and B(see in the below left figure). Show that the line PQ is
the perpendicular bisector of AB.
Q. Line l is the bisector of an angle A and B is any point on
l. BP and BQ are perpendiculars from B to the arms of A
(see the above side figure). Show that:
(i) APB AQB (ii) BP = BQ or B is equidistant from the
arms of A.
Q.In the figure if x = y and AB = CB.
Prove that AE = CD.
Q.In right triangle ABC, right angled at C, M is the mid-point of hypotenuse
AB. C is joined to M and produced to a point D such that DM = CM. Point D is
joined to point B (see the above side figure). Show that:
(i) AMC BMD (ii) DBC is a right angle. (iii) DBC ACB
(iv) CM = 1/2 AB
Q.ABC is a triangle in which altitudes BE and CF to sides
AC and AB are equal (see the below Fig.). Show that (i)
ABE ACF (ii) AB = AC, i.e., ABC is an isosceles
triangle.
Q. In the below Fig, PQ = PR and Q = R.
Prove that PQS PRT
Q. P is a point equidistant from two lines l and m intersecting at point
A (see the above right side figure). Show that the line AP bisects the
angle between them.
Q.
In figure, AC = AE, AB = AD and ∠BAD = ∠EAC.
Show that BC = DE.
Q. ABC and ∆DBC are two isosceles triangles on the same base BC and
vertices A and D are on the same side of BC (see figure). If AD is extended
to intersect BC at P, show that
(i) ∆ABD ≅ ∆ACD
(ii) ∆ABP ≅ ∆ACP
(iii) AP bisects ∠A as well as ∠D
(iv) AP is the perpendicular bisector of BC.
Q.Two sides AB and BC and median AM of one triangle ABC are
respectively equal to sides PQ and OR and median PN of ∆PQR
(see figure). Show that
(i) ∆ABC ≅ ∆PQR
(ii) ∆ABM ≅ ∆PQN
Q.ABC is an isosceles triangle in which altitudes BE and
CF are drawn to equal sides AC and AB respectively (see
figure). Show that these altitudes are equal.
For solutions:
visit-
https://youtu.be/uLnufDv3cKI
