Question

9 finish the triangle proof by dragging the correct reasons to their box. there will be two extra unused reasons! given: d is the midpoint of ac, ∠adb ≅ ∠cdb prove: △abc is isosceles click to add speaker notes

Explanation:

Step1: State the given information

1. \(D\) is the midpoint of \(AC\), \(\angle ADB\cong\angle CDB\) - Reason: Given

Step2: Use the definition of midpoint

1. \(AD = DC\) - Reason: Definition of Midpoint

Step3: Use the reflexive property

1. \(BD=BD\) - Reason: Reflexive Property

Step4: Prove \(\triangle ABD\cong\triangle CBD\)

1. \(\triangle ABD\cong\triangle CBD\) - Reason: \(SAS\) (Since \(AD = DC\), \(\angle ADB\cong\angle CDB\), \(BD = BD\))

Step5: Use CPCTC

1. \(AB = CB\) - Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Step6: Use the definition of isosceles triangle

1. \(\triangle ABC\) is isosceles - Reason: Definition of Isosceles (A triangle with two equal sides (\(AB = CB\)) is isosceles)

Answer:

1. \(D\) is the midpoint of \(AC\), \(\angle ADB\cong\angle CDB\) - Given
2. \(AD = DC\) - Definition of Midpoint
3. \(BD = BD\) - Reflexive Property
4. \(\triangle ABD\cong\triangle CBD\) - \(SAS\)
5. \(AB = CB\) - CPCTC
6. \(\triangle ABC\) is isosceles - Definition of Isosceles