SAS Criteria for Congruency
Trending Questions
Prove that angles opposite to equal sides of an isosceles triangle are equal.
AD is an altitude of an isosceles ΔABC in which AB = AC.Show that (i) AD bisects BC, (ii) AD bisects ∠A.
In ΔABC and ΔDEF, it is given that AB = DE and BC = EF. In order that ΔABC≅ ΔDEF, we must have(a) ∠A=∠D (b) ∠B=∠E (c) ∠C=∠F (d) none of these
Show that the diagonals of a square are equal and bisect each other at right angles.
In the figure, ABC is a triangle in which ∠B=2∠C. D is a point on side BC such that AD bisects ∠BAC and AB=CD. BE is the bisector of ∠B. The measure of ∠BAC is
72∘
73∘
74∘
95∘
If √m + √n - √p = 0 then find value of (m+n-p)^2.
and are equal perpendiculars to a line segment (see Fig.) . Show that bisects .
If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then, the two triangles are congruent by
In a triangle ABC, D is mid-point of BC; AD is produced upto E so that DE = AD. Prove that :
(i) Δ ABD and Δ ECD are congruent.
(ii) AB = EC.
(iii) AB is parallel to EC.
"If two angles and a side of one triangle are equal to two angles and a side of another triangle then the two triangles must be congruent." Is the statement true? Why?
is a point in the interior of a square such that triangle is an equilateral triangle. Show that is an isosceles triangle.
In an isosceles triangle ABC with AB=AC, D and E are points on BC such that BE=CD. The value of ADAE is equal to
1
2
3
4
In the following diagrams, ABCD is a square and APB is an equilateral triangle.
In each case,
(i) Prove that : Δ APD ≅Δ BPC
(ii) Find the angles of Δ DPC.
In the figure, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR=15∘
Question 1
Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
In the given figure, O is a point in the interior of square ABCD such that ΔOAB is an equilateral triangle.Show that ΔOCD is an isosceles triangle.
The line segments joining the midpoints M and N of parallel sides AB and DC respectively of a trapezium ABCD is perpendicular to both the sides AB and DC. Prove that AD = BC.
On the sides AB and AC of triangle ABC, equilateral triangles ABD and ACE are drawn.
Prove that: (i) ∠ CAD = ∠ BAE
(ii) CD = BE.
In an equilateral triangle ABC; points P, Q and R are taken on the sides AB, BC and CA respectively such that AP= BQ = CR. Prove that triangle PQR is equilateral.
A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that : QA =QB.
In a Δ ABC, BD is the median to the side AC, BD is produced to E such that BD = DE.
Prove that : AE is parallel to BC.
CDE is an equilateral triangle formed on a side a CD of a square ABCD. Show that ΔADE≅ ΔBCE.
If two sides and the included angle of a triangle are respectively equal to two sides and the included angle of another triangle, the two triangles are congruent. State True or False.
True
False
- Scalene triangle
- Equilateral triangle
- Right-angled triangle
- Isosceles triangle
In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ΔABC such that AX = AY. Prove that CX = BY.
In the figure, it is given that RT = TS, ∠1=2 ∠2 and ∠4=2 ∠3. Prove that ΔRBT≅SAT.
- ΔABC ≅ ΔADC
- ΔABC ≅ ΔAEC
- ΔAEC ≅ ΔCDE
- ΔABE ≅ ΔCQD
In figure, D and E are points on side BC of the a ΔABC such that BD = CE and AD = AE, show that ΔABD≅ΔAE show that ΔABD≅ΔACE
The perpendicular bisectors of the sides of a triangle ABC meet at I.
Prove that : IA = IB = IC.