Match the reasons with the statements in the proof to prove that triangle axc is congruent to triangle bxc, given that angles 3 and 4 are right angles and ax = bx. given: ∠3 and ∠4 are right angles ax = bx prove: △axc ≅ △bxc 1. ∠3 and ∠4 are right angles reflexive property of equality 2. ax = bx cx = cx leg - leg theorem 3. △axc ≅ △bxc given

The reasons are given below.

Step-by-step explanation:

In triangle ΔAXC and ΔBXC, we are given that angles 3 and 4 are right angles and AX = BX. we have to match the reasons in the given proof of congruency of triangles △AXC ≅ △BXC

In ΔAXC and ΔBXC,

AX=BX               (Given)

∠3 = ∠4 = 90°    (both right angles)

CX=CX           (Common i.e reflexive property of equality)

Hence by SAS similarity theorem  ΔAXC ≅ ΔBXC

hence, the above are the reasons of the statements in given proof.

1.)  ∠3 and ∠4 are right angles, AX = BX     ---    b.) Given

2 ).     CX = CX      ---      a.) Reflexive Property of Equality

3.)  △AXC ≅ △BXC  ---      c.) Leg-Leg Theorem  

Step-by-step explanation:

1.∠3 and ∠4 are right angles, AX = BX  

2 .     CX = CX      

3.△AXC ≅ △BXC

a.Reflexive Property of Equality  

b.     Given

c.    Leg-Leg Theorem  

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: