Question

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1) Given: D is the midpoint of segment A C., segment B D is perpendicular to segment A C. Prove: triangle A D B is congruent to triangle C D B. Refer to the proof above to answer the following 5 questions. What should replace (a) in the proof?

segment A B is congruent to segment C B.

segment A D is congruent to segment D C.

segment B D is congruent to segment A C.

segment A C is congruent to segment A C.
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7.
What should replace (b) in the proof?

Midpoint

Perpendicular lines

Right angles

Right Triangles
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8. What should replace (c) in the proof?

Definition of Perpendicular lines

Definition of Right angles

Definition of Midpoint

Definition of Right triangles
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9. What should replace (d) in the proof?

Symbols for segment A C is congruent to segment A C.

Symbols for segment A B is congruent to segment A B.

Symbols for segment B C is congruent to segment B C.

Symbols for segment B D is congruent to segment B D.
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10. What should replace (e) in the proof?

SSA Postulate

SSS Postulate

LL Theorem

HL Theorem

Answer 1

After D is the midpoint of AC we write

(a) AD  congruent to DC

Angle ADB and angle CDB are both

(b) right angles

because of the

(c) definition of perpendicular lines

The reflexive property means a thing equals itself. The common side in both triangles is BD, so we write

(d) BD is congruent to BD

Now we have a right triangle with two pair of congruent legs, so by the Leg Leg Theorem we can conclude triangles ADB and CDB are congruent

(e) LL

We could have also answered SAS, Side Angle Side for (e) but it's not one of the choices.   SSA is not the same thing, and not a postulate.