You decide to challenge 6 of your closest friends to a marathon with your best friend. Since you and your friend are running together you decided to get matching t-shirts. On the day of the race, you and your friend showed up with matching math t-shirts. Co-incidentally your friends also showed up with matching t-shirts. A pair of your friendsshowed up with Red Sox t-shirts. Another pair waltzed in with Patriots t-shirts. The lastpair of your friends walked in with Golden State Warrior t-shirts. At the end of the race,(a) 1 runner between the Math friends(b) 2 runners between the Red Sox pair(c) 3 runners between the Golden State Warrior pair(d) 4 runners between the Patriot pair. If we know that the last runner wore a patriot shirt, can you tell what the order of therunners finished in from fastest to slowest?

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)