Advertisements
Advertisements
प्रश्न
From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.

Advertisements
उत्तर
In △ABC and △QPR
AB = PQ ...(Given)
BC = PR ...(Given)
∠BAC = ∠PQR = 90∘ ...(Given)
∴ ΔBAC ≅ ΔPQR ...[Hypotenuse side test]
∴ seg AC ≅ seg QR ...[c.s.c.t.]
∠ABC ≅ ∠QPR and ∠ACB ≅ ∠QRP ...[c.a.c.t.]
APPEARS IN
संबंधित प्रश्न
Complete the congruence statement:
ΔBCA ≅?
ΔQRS ≅?

In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
In a squared sheet, draw two triangles of equal areas such that
The triangles are not congruent.
What can you say about their perimeters?
Mark the correct alternative in each of the following:
If ABC ≅ ΔLKM, then side of ΔLKM equal to side AC of ΔABC is
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is

In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is

In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.

In the following diagram, ABCD is a square and APB is an equilateral triangle.
(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.
State, whether the pairs of triangles given in the following figures are congruent or not:

Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).
A is any point in the angle PQR such that the perpendiculars drawn from A on PQ and QR are equal. Prove that ∠AQP = ∠AQR.
ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.
∆ABC and ∆PQR are congruent under the correspondence:
ABC ↔ RQP
Write the parts of ∆ABC that correspond to
(i) `bar"PQ"`
(ii)∠Q
(iii) `bar"RP"`
ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
If ∆PQR is congruent to ∆STU (see figure), then what is the length of TU?

The top and bottom faces of a kaleidoscope are congruent.
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆ABC ≅ ∆LMN
