28. Error Analysis To prove that Δ P Q R cap delta p q r  is isosceles, a student began by stating that since Q is on the segment perpendicular to P R ¯ , p r bar , comma  Q is equidistant from the endpoints of P R ¯ . p r bar , .  What is the error in the student's reasoning?

    

Writing Determine whether A must be on the bisector of ∠ T X R . angle t x r .  Explain.

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32. Proof Prove the Perpendicular Bisector Theorem.

    Given: P M ↔ ⊥ A B ¯ , P M ↔ modified p m with left right arrow above , up tack , eh b bar , comma . modified p m with left right arrow above  bisects A B ¯ eh b bar

    Prove: A P = B P eh p equals b p

    

33. Proof Prove the Converse of the Perpendicular Bisector Theorem.

    Given: P A = P B p eh equals p b  with P M ¯ ⊥ A B ¯ p m bar , up tack , eh b bar  at M.

    Prove: P is on the perpendicular bisector of A B ¯ . eh b bar , .

    

34. Proof Prove the Angle Bisector Theorem.

    Given: Q S → q s vector  bisects ∠ P Q R , angle p q r comma

    S P ¯ ⊥ Q P → , S R ¯ ⊥ Q R → s p bar , up tack , q p vector . comma , s r bar , up tack , q r vector

    Prove: S P = S R s p equals s r

    

35. Proof Prove the Converse of the Angle Bisector Theorem.

    Given: S P ¯ ⊥ Q P → , S P ¯ ⊥ Q R → , s p bar , up tack , q p vector , comma . s p bar , up tack , q r vector , comma

    S P = S R s p equals s r

    Prove: Q S → q s vector  bisects ∠ P Q R . angle p q r .

    

36. Coordinate Geometry Use points A(6, 8), O(0, 0), and B(10, 0).
    1. Write equations of lines l and m such that l ⊥ O A ↔ l up tack , modified o eh with left right arrow above  at A and m ⊥ O B ↔ m up tack , modified o b with left right arrow above  at B.
    2. Find the intersection C of lines l and m.
    3. Show that C A = C B . c eh equals c b .
    4. Explain why C is on the bisector of ∠ A O B . angle eh o b .

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