Question 7

c is the circumcenter of isosceles triangle abd with vertex angle ∠abd. does the following proof correctly justify that triangles abe and dbe are congruent?

it is given that triangle abd is an isosceles triangle, so segments ab and db are congruent by the definition of isosceles triangle.
it is given that c is the circumcenter of triangle abd, making segment be a perpendicular bisector.
by the definition of perpendicular, angles aeb and deb are 90°, so triangles abe and deb are right triangles.
triangles abe and deb share side ad making it congruent to itself by the reflexive property.
triangles abe and dbe are congruent by hl.

triangle abd with segments bc, dc, and ac drawn from each vertex and meeting at point c inside triangle abd, segment bc is extended past c with dashed lines so that it intersects with side ad at point e.

a) there is an error in line 1; segments ab and bd are given to be congruent.
b) there is an error in line 4; segment ad is not a shared side.
c)there is an error in line 3; segment be should be a median.
d)the proof is correct.

question 8

what conclusion can be made for c and e?

triangle abc has side ab measuring c, side bc measuring 4 units, and angle acb measuring 36 and a half degrees. triangle abc is connected to triangle acd by shared side ac. triangle acd has side ad measuring e and angle acd measuring 27 and 8 tenths degrees. segments bc, ac, and dc are marked congruent.

a) c ≥ e
b) c ≤ e
c)c > e
d) c < e
question 9

a land surveyor places two stakes 500 ft apart and creates a perpendicular to the line that connects these two stakes. he needs to place a third stake 100 ft away that is equidistant to the two original stakes. to apply the perpendicular bisector theorem, the land surveyor would need to identify

a line parallel to the line connecting the two stakes
a line that is parallel to the perpendicular line
the midpoint along the line connecting the two stakes
the midpoint along the line that is perpendicular to the line connecting the two stakes

question 10

alex is writing statements to prove that the sum of the measures of interior angles of triangle pqr is equal to 180°. line m is parallel to line n.

line n is parallel to line m. triangle pqr has vertex p on line n and vertices q and r on line m. angle qpr is 80 degrees. segment pq makes 40 degrees angle with line n and segment pr makes 60 degrees angle with line n.

which is a true statement he could write?

a) angle prq measures 40°.
b) angle pqr measures 60°.
c)angle prq measures 80°.
d)angle pqr measures 40°.