Answer:
∠ABD ≅ ∠CBD
Step-by-step explanation:
<u>Given: </u>line segment AB ≅ line segment BC
<u>Prove:</u> The base angles of an isosceles triangle are congruent.
Statement Reason
1. Segment BD is an angle bisector of ∠ABC - By construction
2. ∠ABD ≅ ∠CBD - Definition of an Angle Bisector
3. Segment BD ≅ segment BD - Reflexive Property
4. ΔABD ≅ ΔCBD - Side-Angle-Side (SAS) Postulate
5. ∠BAC ≅ ∠BCA - CPCTC
Answer:
<1=54, <2=36, <3=90, <4=36
Step-by-step explanation:
in the rhombus shown, there are 4 congruent right triangles because the disgonals of a rhombus are perpendicular and the sides of a rhombus are congruent. We already know that the larger acute angles are all 54 degrees and we can use triangle sum to find that the smaller acute angles are all 36 degrees. Obviously the right angles are 90 degrees, so we can look at the picture and find the marked angles.