A carpenter adds a diagonal brace to a rectangle frame as shown. If the carpenter wants the triangles on either side of the brace to be congruent,
what should be the measure of 23?

The volume of the sun is approximately 1 × 10^18 cu km, while the volume of jupiter is approximately 1 × 10^15 cu km. which of the following is true? a. the volume of jupiter is approximately one thousand times the volume of the sun. b. the volume of jupiter is approximately one hundred times the volume of the sun. c. the volume of the sun is approximately one thousand times the volume of jupiter. d. the volume of the sun is approximately one hundred times the volume of jupiter.

Find the distance between the pair of points a(-1,8) and b(-8,4)

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality