Mathematics
In the given figure,
AC = CD
AB > CD
AB < CD
none of these
Triangles
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Answer
Since, AB = AC.
∴ ∠ABC = ∠ACB = 70° (As angles opposite to equal sides of an isosceles triangle are equal.)
From figure,
⇒ ∠ACB + ∠ACD = 180° [Linear pairs]
⇒ 70° + ∠ACD = 180°
⇒ ∠ACD = 110°.
In △ACD,
⇒ ∠CAD + ∠ADC + ∠ACD = 180°
⇒ ∠CAD + 40° + 110° = 180°
⇒ ∠CAD + 150° = 180°
⇒ ∠CAD = 30°.
In △ACD,
∠ADC = 40°
∠CAD = 30°
∴ ∠ADC > ∠CAD
∴ AC > CD (As side opposite to greater angle is greater.)
Since, AB = AC,
∴ AB > CD.
Hence, option 2 is the correct option.
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Related Questions
Triangles ABC is equilateral and BC = CE, then angle AEC is:
60°
45°
30°
120°
Side BA is produced upto point D and side BC upto point E such that ∠DAC = 110° and ∠ACE = 125°. Then the largest side of the triangle ABC is
AB
BC
AC
none of these
Statement (1): In the given figure, AC = DC = BD and ∠B = 30°.
Statement (2): ΔCAD is equilateral.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Statement (1): AB = AC and D is any point on side BC of triangle ABC.
Statement (2): AB > AD.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.