Answered

Find expert answers and community support for all your questions on IDNLearn.com. Explore a wide array of topics and find reliable answers from our experienced community members.

Geometry Question: If the median to a side is a triangle is also an altitude to that side, then the triangle is isosceles. (#8 in picture)

Geometry Question If The Median To A Side Is A Triangle Is Also An Altitude To That Side Then The Triangle Is Isosceles 8 In Picture class=

Sagot :

8.

A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. So:

[tex]\begin{gathered} AM\cong MB \\ MC\cong CM_{\text{ }}Reflexive_{\text{ }}property \\ m\angle AMC\cong m\angle BMC_{\text{ }}Perpendicular_{\text{ }}bisector \end{gathered}[/tex]

Therefore:

[tex]\Delta AMC\cong\Delta BMC_{\text{ }}SAS_{\text{ }}Theorem[/tex][tex]m\angle CAM\cong\angle CBM_{\text{ }}CPCTC[/tex]

We can conclude that:

[tex]\Delta ABC[/tex]

Is an isosceles triangle

View image AumB339884
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.