Question

If DEF=GJH, find each missing measure

Answer 1

Congruent triangles have equal corresponding sides and angles.

• The measure of the side lengths are: $\mathbf{DF = 16m}$, $\mathbf{JH = 14m}$ and $\mathbf{GJ = 19m}$
• The measure of the angles are: $\mathbf{\angle G = 34^o}$, $\mathbf{\angle J = 41^o}$ and $\mathbf{\angle F = 105^o}$

The given parameters are:

$\mathbf{\triangle D EF \cong \triangle GJH}$

$\mathbf{EF = 14m}$

$\mathbf{D E = 19m}$

$\mathbf{GH = 16m}$

$\mathbf{\angle D = 34^o}$

$\mathbf{\angle H = 105^o}$

$\mathbf{\triangle D EF \cong \triangle GJH}$ means that triangles DEF and GHJ are congruent triangles.

So, we have:

$\mathbf{DF = GH}$

This gives

$\mathbf{DF = 16m}$

Also, we have:

$\mathbf{JH = EF}$

This gives

$\mathbf{JH = 14m}$

Also, we have:

$\mathbf{GJ = DE}$

This gives

$\mathbf{GJ = 19m}$

The following angles are also congruent

$\mathbf{\angle F = \angle H}$

This gives

$\mathbf{\angle F = 105^o}$

Also, we have:

$\mathbf{\angle G = \angle D}$

This gives

$\mathbf{\angle G = 34^o}$

The measure of angle J is then calculated using

$\mathbf{\angle J + \angle H + \angle G = 180^o}$

This gives

$\mathbf{\angle J + 105 + 34= 180^o}$

$\mathbf{\angle J + 139= 180^o}$

Subtract 139 from both sides

$\mathbf{\angle J = 41^o}$

Read more about congruent triangles at:

brainly.com/question/4364353