Advertisements
Advertisements
Question
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is
Options
70°
110°
120°
130°
Advertisements
Solution
We have to find the value of ∠ABD in the following figure.
It is given that
∠MAE = 70°
∠NAC = 70°(Vertically apposite angle)
Now ∠MAE + ∠EAB + ∠BAC =180° (linear pair) …… (1)
Similarly ∠EAB +∠BAC +∠NAC = 180° (linear pair) …… (2)
From equation (1) we have
∠EAB + ∠BAC = 180°
= 110°
Now ∠FCA = ∠DBA (same exterior angle)
∠ACF = ∠EAC (Interior angle)
Now
∠EAC = 110°
So ∠AFC = 110°
Since ∠AFC =∠ABD
Hence (b)∠ABD = 110°.
APPEARS IN
RELATED QUESTIONS
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 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.
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) AM = AN (ii) ΔAMC ≅ ΔANB
State, whether the pairs of triangles given in the following figures are congruent or not:
Δ ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80° and Δ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(BC = 5cm,AC = 6cm,∠C = 80°);
ΔXYZ;(XZ = 6cm,XY = 5cm,∠X = 70°).
In the figure, ∠CPD = ∠BPD and AD is the bisector of ∠BAC. Prove that ΔCAP ≅ ΔBAP and CP = BP.
In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.
AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.
ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
