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
In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =
In the following example, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.
By ______ test
Δ ABC ≅ ΔPQR
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that:
- ∠CAD = ∠BAE
- CD = BE
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) BN = CM (ii) ΔBMC ≅ ΔCNB
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;(∠B = 90°,BC = 6cm,AB = 8cm);
ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).
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.
In the figure, ∠CPD = ∠BPD and AD is the bisector of ∠BAC. Prove that ΔCAP ≅ ΔBAP and CP = BP.
In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.Prove that BO = CO and the ray AO is the bisector of angle BAC.
ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.
Prove that
(i) BG = CH
(ii) AG = AH
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles
It is given that ∆ABC ≅ ∆RPQ. Is it true to say that BC = QR? Why?
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 congruent figures super impose each other completely.
