Advertisements
Advertisements
Question
In the given figure, prove that:
CD + DA + AB + BC > 2AC
Advertisements
Solution
We have to prove that CD + DA + AB + BC > 2AC
In ΔABC we have
AB + BC > AC (As sum of two sides of triangle is greater than third one) ........(1)
In ΔACDwe have
AD + CD > AC (As sum of two sides of triangle is greater than third one) .........(2)
Hence
Adding (1) & (2) we get AB + BC + AC + CD > 2AC Proved.
APPEARS IN
RELATED QUESTIONS
In the figure, the two triangles are congruent.
The corresponding parts are marked. We can write ΔRAT ≅ ?
In two triangles ABC and ADC, if AB = AD and BC = CD. Are they congruent?
The given figure shows a circle with center O. P is mid-point of chord AB.
Show that OP is perpendicular to AB.
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD.
Prove that :
(i) ΔABD and ΔECD are congruent.
(ii) AB = CE.
(iii) AB is parallel to EC
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD. Prove that:
AB is parallel to EC.
If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.
In the given figure, AB = DB and Ac = DC.
If ∠ ABD = 58o,
∠ DBC = (2x - 4)o,
∠ ACB = y + 15o and
∠ DCB = 63o ; find the values of x and y.
In the following figures, the sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and median PS of the triangle PQR.
Prove that ΔABC and ΔPQR are congruent.
 |
 |
ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such produced to E and F respectively, such that AB = BE and AD = DF.
Prove that: ΔBEC ≅ ΔDCF.
AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides of AB prove that CD bisects AB.
