Mathematics
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.
Triangles
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Answer
In ΔBDC,
⇒ DC = DB
⇒ ∠DBC = ∠DCB = 30° (Angles opposite to equal sides of a triangle are always equal)
In ΔBDC, according to angle sum property,
⇒ ∠BDC + ∠DBC + ∠DCB = 180°
⇒ ∠BDC + 30° + 30° = 180°
⇒ ∠BDC + 60° = 180°
⇒ ∠BDC = 180° - 60°
⇒ ∠BDC = 120°
Since ∠BDC and ∠CDA forms linear pair.
⇒ ∠BDC + ∠CDA = 180°
⇒ 120° + ∠CDA = 180°
⇒ ∠CDA = 180° - 120°
⇒ ∠CDA = 60°
Since, AC = DC
⇒ ∠CDA = ∠CAD = 60° (Angles opposite to equal sides of a triangle is always equal)
In ΔACD, according to angle sum property,
⇒ ∠ACD + ∠CDA + ∠CAD = 180°
⇒ ∠ACD + 60° + 60° = 180°
⇒ ∠ACD + 120° = 180°
⇒ ∠ACD = 180° - 120°
⇒ ∠ACD = 60°
So, ΔCAD is equilateral.
∴ Both the statements are true.
Hence, option 1 is the correct option.
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Related Questions
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
In the given figure,
AC = CD
AB > CD
AB < CD
none of these
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.
Assertion (A): In the given figure, AB = BC and AD = CE, then BD = CE.
Reason (R): ΔBAD ≅ ΔBCE by SAS.
A is true, but R is false.
A is false, but R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.