Pedro is going to use SAS to prove that ΔPQR ≅ ΔSQR. Which of these…

Pedro is going to use SAS to prove that ΔPQR ≅ ΔSQR. Which of these is a necessary step in Pedro’s proof? A. Prove that ∠QPR ≅ ∠QSR by the Isosceles Triangle Theorem. B. Prove that QR ≅ QR by the reflexive property. C. Prove that PQ ≅ SQ by CPCTC. D. Prove that ∠PQR ≅ ∠SQR by vertical angles.

The correct answer is B.

Explanation

  • To use SAS you need two pairs of corresponding sides and the included angle between them. A common and necessary step is to note the shared side:

QR ≅ QR (reflexive property).

  • Why the others are wrong:
  • A: The Isosceles Triangle Theorem applies only if you already know a triangle is isosceles; nothing in the statement guarantees that, so it’s not a necessary step.
  • C: CPCTC (corresponding parts of congruent triangles are congruent) can only be used after the triangles are proven congruent — you cannot use it to prove congruence.
  • D: ∠PQR and ∠SQR are adjacent angles that share side QR, not vertical angles, so you cannot claim they’re equal by the vertical-angles theorem.

Therefore showing QR ≅ QR by the reflexive property is a necessary step for a SAS proof.

100% (3 rated)

Related

Which of the following statements is true? If more than one statement is true, identify all the statements which are true. [ 1 point for identifying all true statements, ‐ 0 . 5 points for choosing a wrong combination even if some of the statements chosen are true, 0 points for not answering ] ( i ) An all ‐ pass filter passes through all frequencies unchanged, but can change the phase of the signal ( ii ) If the FIR filter coefficients are symmetric, then it has linear phase ( iii ) FIR filter is computationally more efficient than an IIR filter of comparable performance ( iv ) A filter that does not operate in real ‐ time can be non ‐ causal

A game is said to be fair if the expected value (after considering the cost) is 0. This means that in the long run, both the player and the “house” would expect to win nothing. If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a carnival, you pay $1 to choose a card from a standard deck. If you choose a red card, you double your money, but if you pick a black card, you do not get any. (A standard deck of cards has 52 cards. 26 of the cards are red.)

Calculating tax incidence Suppose that the U.S. government decides to charge cola consumers a tax. Before the tax, 10,000 cases of cola were sold every week at a price of $5 per case. After the tax, 3,000 cases of cola are sold every week; consumers pay $8 per case (including the tax), and producers receive $3 per case. 1) The amount of the tax on a case of cola is $??? per case. 2) Of this amount, the burden that falls on consumers is $??? per case, and the burden that falls on producers is ???$ per case. 3) True or False: The effect of the tax on the quantity sold would have been the same as if the tax had been levied on producers. True/ False