Answer:

Step-by-step explanation:



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We can identify that the missing reason in the proof is: Definition of Congruent angles.
<h3>How to give proof of a congruent triangle?</h3>
We know that an angle measure of 90° of ∠ABC in the triangle means that it is a right angle triangle.
We also see that ∠ADB is also a right angle and is equal to 90°.
Now, since they have exactly the same measure, these angles are congruent. Then we can say that the angles are congruent and as such:
∠ABC ≅ ∠ABD
Thus, we can identify that the missing reason is: Definition of Congruent angles.
Read more about Triangle proof at; brainly.com/question/1248322
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Answer:
63.5
Step-by-step explanation:
The diagonals of a rhombus bisect opposite angles.
The longer diagonal bisects the 42° angle
The larger angle of the rhombus is 180 - 42 = 138
Let x = the length of the longer diagonal
You know two sides and the included angle of a triangle.
Using the law of cosines we get

x^2 = 34^2 + 34^2 - 2(34)(34) cos 138
= 1156 + 1156 - 2312 c0s 138
= 4030.1508...
x = sq rt 4030.1508...
= 63.5