Given: δabc is an isosceles triangle where ab = bc. prove: m∠bac = m∠bca proof: statement reason 1. let δabc be an isosceles triangle where ab = bc. given 2. create point d on so that bisects ∠abc as shown. constructing an angle bisector 3. m∠abd = m∠dbc definition of angle bisector 4. bd = bd 5. δabd ≅ δcbd sas 6. m∠bac = m∠bca corresponding angles of congruent triangles are equal. what is the reason for statement 4 in this proof? a. transitive property of equality b. definition of midpoint c. definition of parallel lines d. reflexive property of equality

The avenues in a particular city run north to south and are numbered consecutively with 1st avenue at the western border of the city. the streets in the city run east to west and are numbered consecutively with 1st street at the southern border of the city. for a festival, the city is not allowing cars to park in a rectangular region bordered by 5th avenue to the west. 9th avenue to the east, 4th street to the south, and 6th street to the north. if x is the avenue number and yis the street number, which of the following systems describes the region in which cars are not allowed to park? 5th ave 9th ave

Triangle xyz, with vertices x(-2, 0), y(-2, -1), and z(-5, -2), undergoes a transformation to form triangle x? y? z? , with vertices x? (4, -2), y? (4, -3), and z? (1, -4). the type of transformation that triangle xyz undergoes is a . triangle x? y? z? then undergoes a transformation to form triangle x? y? z? , with vertices x? (4, 2), y? (4, 3), and z? (1, 4). the type of transformation that triangle x? y? z? undergoes is a .

Add: (6x^2-5x+3) + (3x^3+7x-8) a. 9x^2+12x-5 b. 9x^2+2x+11 c. 9x^2+2x-5 d. 9x^2-2x+5