Advertisements
Advertisements
प्रश्न
`square`ABCD is trapezium, AB || CD diagonals of trapezium intersects in point P.
Write the answers of the following questions:
- Draw the figure using the given information.
- Write any one pair of alternate angles and opposite angles.
- Write the names of similar triangles with the test of similarity.
उत्तर
- Alternate angles: ∠BAP = ∠PCD ...(∵ AB || DC and BD is their transversal.)
Opposite angles: ∠APB = ∠CPD ...(Vertically opposite angles) - ΔAPB ∼ ΔCPD ...(AA test of similarity)
APPEARS IN
संबंधित प्रश्न
S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ∼ ΔRTS.
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔABD ∼ ΔCBE
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔAEP ∼ ΔADB
If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR, prove that `("AB")/("PQ") = ("AD")/("PM")`.
In the given figure, two chords AB and CD intersect each other at the point P. prove that:
(i) ΔAPC ∼ ΔDPB
(ii) AP.BP = CP.DP
In the following figure, AB || QR. Find the length of PB.
In the following Figure, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.
The sides of certain triangles are given below. Determine which of them right triangles are.
1.6cm, 3.8cm, 4cm
In the figure, if DE∥BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals ______.
If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?
In figure, if AB || DC and AC and PQ intersect each other at the point O, prove that OA . CQ = OC . AP
If in triangles ABC and DEF, `(AB)/(DE) = (BC)/(FD)`, then they will be similar, when ______.
In figure, if ∠D = ∠C, then it is true that ΔADE ~ ΔACB? Why?
In figure, l || m and line segments AB, CD and EF are concurrent at point P. Prove that `(AE)/(BF) = (AC)/(BD) = (CE)/(FD)`.
In the given figure, ΔPQR is a right-angled triangle with ∠PQR = 90°. QS is perpendicular to PR. Prove that pq = rx.
A tangent ADB is drawn to a circle at D whose centre is C. Also, PQ is a chord parallel to AB and ∠QDB = 50°. Find the value of ∠PDQ.
The sum of two angles of a triangle is 150°, and their difference is 30°. Find the angles.
If ΔABC ~ ΔDEF and ∠A = 47°, ∠E = 83°, then ∠C is equal ______.
If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?