Advertisements
Advertisements
प्रश्न
In the figure, BC = CE and ∠1 = ∠2. Prove that ΔGCB ≅ ΔDCE.
Advertisements
उत्तर
In ΔGCB and ΔDCE and
∠1 + ∠GBC = ∠2 + ∠DEC = 180°
∠1 = ∠2 =
⇒ ∠GBC = ∠DEC
BC = CE
∠GCB = ∠DCE = ...(vertically opposite angles)
Therefore,
ΔGCB ≅ ΔDCE ....(ASA criteria).
APPEARS IN
संबंधित प्रश्न
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
Observe the information shown in pair of triangle given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
From the information shown in the figure,
in ΔPTQ and ΔSTR
seg PT ≅ seg ST
∠PTQ ≅ ∠STR ...[Vertically opposite angles]
∴ ΔPTQ ≅ ΔSTR ...`square` test
∴ `{:("∠TPQ" ≅ square),("and" square ≅ "∠TRS"):}}` ...corresponding angles of congruent triangles
seg PQ ≅ `square` ...corresponding sides of congruent triangles
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.
In the following figure, OA = OC and AB = BC.
Prove that:
(i) ∠AOB = 90o
(ii) ΔAOD ≅ ΔCOD
(iii) AD = CD
In the given figure, prove that: ∆ ABD ≅ ∆ ACD
State, whether the pairs of triangles given in the following figures are congruent or not:
In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:
a. DABD andDECD are congruent.
b. AB = EC
c. AB is parallel to EC
ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.
Prove that
(i) BG = CH
(ii) AG = AH
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.
