Ioana tried to prove that \triangle OPQ\cong \triangle SRQ△OPQ≅△SRQtriangle, O, P, Q, \cong, triangle, S, R, Q. Statement Reason 1 PQ=RQ=9PQ=RQ=9P, Q, equals, R, Q, equals, 9 Given 2 m\angle O=m\angle S=90\degreem∠O=m∠S=90°m, angle, O, equals, m, angle, S, equals, 90, degree Given 3 m\angle PQO=m\angle RQS=63\degreem∠PQO=m∠RQS=63°m, angle, P, Q, O, equals, m, angle, R, Q, S, equals, 63, degree Given 4 \triangle OPQ\cong \triangle SRQ△OPQ≅△SRQtriangle, O, P, Q, \cong, triangle, S, R, Q Angle-side-angle congruence What is the first error Ioana made in her proof? Choose 1 answer: Choose 1 answer: (Choice A) A Ioana used an invalid reason to justify the congruence of a pair of sides or angles. (Choice B) B Ioana only established some of the necessary conditions for a congruence criterion. (Choice C) C Ioana established all necessary conditions, but then used an inappropriate congruence criterion. (Choice D) D Ioana used a criterion that does not guarantee congruence.

Answer:

The answer is Choice C

Step-by-step explanation:

I got it right, look at the screenshot for proof

Answer:

Choice C

Step-by-step explanation:

Writing a proof

A proof is a formal description of how we can know that something is true based on the information from a mathematical scenario.

Each step of the proof is a transformation, a construction, or a statement about what we can conclude from earlier steps.

For a two-column proof we give a reason to justify each statement. Common reasons include geometric theorems, algebraic properties, and information given in diagrams.

Let's check the reason for each step and whether Ioana established the conditions for it.

Hint #22 / 4

Step 1

The diagram does support the claim that PQ=RQ=9PQ=RQ=9P, Q, equals, R, Q, equals, 9.

Step 1 is correct.

Step 2

The diagram does support the claim that m\angle O=m\angle S=90\degreem∠O=m∠S=90°m, angle, O, equals, m, angle, S, equals, 90, degree.

Step 2 is correct.

Step 3

The diagram does support the claim that m\angle PQO=m\angle RQS=63\degreem∠PQO=m∠RQS=63°m, angle, P, Q, O, equals, m, angle, R, Q, S, equals, 63, degree.

Step 3 is correct.

Hint #33 / 4

Step 4

In this step, Ioana claims that \triangle OPQ\cong \triangle SRQ△OPQ≅△SRQtriangle, O, P, Q, \cong, triangle, S, R, Q using the angle-side-angle criterion. But the corresponding pair of congruent sides, \overline{PQ}

PQ

​

start overline, P, Q, end overline and \overline{RQ}

RQ

​

start overline, R, Q, end overline, aren't the sides that are included between the two pairs of congruent corresponding angles.

Ioana should have used the angle-angle-side criterion.

Hint #44 / 4

Ioana established all necessary conditions, but then used an inappropriate congruence criterion.

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2.
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Previous

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